second order hyperbolic s p d e s driven by homogeneous gaussian noise on a hyperplane we study a class of hyperbolic stochastic partial di erential equations in euclidean space that includes the wave equation and the telegraph equation driven by gaussian noise concentrated on a hyperplane the noise is assumed to be white in time but spatially homogeneous within the hyperplane two natural notions of solutions are function valued solutions and random field solutions for the linear form of the equations we identify the necessary and sufficient condition on the spectral measure of the spatial covariance for existence of each type of solution and it turns out that the conditions di er in spatial dimensions 2 and 3 under the condition for existence of a random field solution to the linear form of the equation we prove existence and uniqueness of a random field solution to non linear forms of the equation

reflected mean field backward stochastic differential equations approximation and associated nonlinear pdes abstract mathematical mean field approaches have been used in many fields not only in physics and chemistry but also recently in finance economics and game theory in this paper we will study a new special mean field problem in a purely probabilistic method to characterize its limit which is the solution of mean field backward stochastic differential equations bsdes with reflections on the other hand we will prove that this type of reflected mean field bsdes can also be obtained as the limit equation of the mean field bsdes by penalization method finally we give the probabilistic interpretation of the nonlinear and nonlocal partial differential equations with the obstacles by the solutions of reflected mean field bsdes

almost sure exponential behavior of a directed polymer in a fractional brownian environment this paper studies the asymptotic behavior of a one dimensional directed polymer in a random medium the latter is represented by a gaussian field bh on r r with fractional brownian behavior in time hurst parameter h and arbitrary function valued behavior in space the partition function of such a polymer is u t eb exp 0tbh dr br here b is a continuous time nearest neighbor random walk on z with fixed intensity 2 defined on a complete probability space pb independent of bh the spatial covariance structure of bh is assumed to be homogeneous and periodic with period 2 for h 12 we prove that the upper and lower almost sure limits lim supt t 2hlogu t and lim inft t 2hlogt logu t are non trivial in the sense that they are bounded respectively above and below by finite strictly positive constants thus as h passes through 12 the exponential behavior of u t changes abruptly this can be considered as a phase transition phenomenon novel tools used in this paper include sub gaussian concentration theory via the malliavin calculus detailed analyses of the long range memory of fractional brownian motion and an almost superadditivity property

superdiffusivity for a brownian polymer in a continuous gaussian environment this paper provides information about the asymptotic behavior of a one dimensional brownian polymer in random medium represented by a gaussian field w on r r assumed to be white noise in time and function valued in space according to the behavior of the spatial covariance of w we give a lower bound on the power growth wandering exponent of the polymer when the time parameter goes to infinity the polymer is proved to be superdiffusive with a wandering exponent exceeding any 3 5

serially concatenated continuous phase modulation with iterative decoding serially concatenated and interleaved continuous phase modulation cpm with iterative decoding is investigated an a posteriori probability app algorithm for cpm is developed based on the classic app algorithm for channel codes the system is analyzed through upper bounds on the average bit error probability for coded and interleaved minimum shift keying the weight spectrum is computed resulting in a transfer function bound this is cumbersome for a general cpm system instead only the most significant error events contributing to the weight spectrum are identified simulations show that firstly these events give a satisfactory view of system performance when equal outer codes are used and secondly that remarkably good performance can be obtained for some simple systems finally power spectral densities and bandwidths are computed allowing for a bandwidth performanee comparison of different combinations

moments and growth indices for the nonlinear stochastic heat equation with rough initial conditions we study the nonlinear stochastic heat equation in the spatial domain r driven by space time white noise a central special case is the parabolic anderson model the initial condition is taken to be a measure on r such as the dirac delta function but this measure may also have noncompact support and even be nontempered e g with exponentially growing tails existence and uniqueness of a random field solution is proved without appealing to gronwall s lemma by keeping tight control over moments in the picard iteration scheme upper bounds on all pth moments p 2 are obtained as well as a lower bound on second moments these bounds become equalities for the parabolic anderson model when p 2 we determine the growth indices introduced by conus and khoshnevisan probab theory related fields 152 2012 681 701

linear receivers for correlatively coded msk in this paper we show that many spectrally efficient modified msk schemes termed generalized msk although not representable as oqpsk may nevertheless be suboptimally demodulated using an i q receiver with a proper choice of carrier phase offset correlatively coded msk schemes with i q receivers are studied and it is concluded that duobinary msk and 1 2d d 2 4 msk represent good performance bandwidth tradeoffs among first and second order correlative coding polynomial schemes the optimal design of these receivers are considered subject to the constraint of a finite duration impulse response especially for asymptotic cases of arbitrarily small and large snr filter design based on a zero intersymbol interference constraint for pam based approximations of the signals is also considered the optimized linear i q receivers for 1 d 2 msk and 1 d 2 4 msk are presented these receivers are only 0 28 and 1 24 db poorer than the optimal viterbi receivers at high snr

a faster combinatorial approximation algorithm for scheduling unrelated parallel machines we consider the problem of scheduling n independent jobs on m unrelated parallel machines without preemption job i takes processing time p i j on machine j and the total time used by a machine is the sum of the processing times for the jobs assigned to it the objective is to minimize makespan the best known approximation algorithms for this problem compute an optimum fractional solution and then use rounding techniques to get an integral 2 approximation in this paper we present a combinatorial approximation algorithm that matches this approximation quality it is much simpler than the previously known algorithms and its running time is better this is the first time that a combinatorial algorithm always beats the interior point approach for this problem our algorithm is a generic minimum cost flow algorithm without any complex enhancements tailored to handle unsplittable flow it pushes unsplittable jobs through a two layered bipartite generalized network defined by the scheduling problem in our analysis we take advantage from addressing the approximation problem directly in particular we replace the classical technique of solving the lp relaxation and rounding afterwards by a completely integral approach we feel that this approach will be helpful also for other applications

approximation algorithms for scheduling unrelated parallel machines we consider the following scheduling problem there arem parallel machines andn independent jobs each job is to be assigned to one of the machines the processing of jobj on machinei requires timep ij the objective is to find a schedule that minimizes the makespan our main result is a polynomial algorithm which constructs a schedule that is guaranteed to be no longer than twice the optimum we also present a polynomial approximation scheme for the case that the number of machines is fixed both approximation results are corollaries of a theorem about the relationship of a class of integer programming problems and their linear programming relaxations in particular we give a polynomial method to round the fractional extreme points of the linear program to integral points that nearly satisfy the constraints in contrast to our main result we prove that no polynomial algorithm can achieve a worst case ratio less than 3 2 unlessp np we finally obtain a complexity classification for all special cases with a fixed number of processing times

the stochastic wave equation in two spatial dimensions keywords stochastic wave equation gaussian noise process solution reference prob article 1998 001view record in web of science record created on 2008 12 01 modified on 2017 05 12

random attractor for the 3d viscous primitive equations driven by fractional noises abstract we develop a new and general method to prove the existence of the random attractor strong attractor for the primitive equations pes of large scale ocean and atmosphere dynamics under non periodic boundary conditions and driven by infinite dimensional additive fractional wiener processes in contrast to our new method the common method compact sobolev embedding theorem is to obtain the time uniform a priori estimates in some sobolev space whose regularity is higher than the solution space but this method can not be applied to the 3d stochastic pes with the non periodic boundary conditions therefore the existence of universal attractor weak attractor was established in previous works see 15 16 the main idea of our method is that we first derive that p almost surely the solution operator of stochastic pes is compact then we construct a compact absorbing set by virtue of the compact property of the solution operator and the existence of a absorbing set we should point out that our method has some advantages over the common method of using compact sobolev embedding theorem i e using our method we only need to obtain time uniform a priori estimates in the solution space to prove the existence of random attractor for the corresponding stochastic system while the common method need to establish time uniform a priori estimates in a more regular functional space than the solution space take the stochastic pes for example as the unique strong solution to the stochastic pes belongs to c 0 t h 1 3 in view of our method we only need to obtain the time uniform a priori estimates in the solution space h 1 3 to prove the existence of random attractor for this stochastic system while the common method need to establish time uniform a priori estimates for the solution in the functional space h 2 3 however time uniform a priori estimates in h 2 3 for the solution to stochastic pes are too difficult to be established the present work provides a general way for proving the existence of random attractor for common classes of dissipative stochastic partial differential equations driven by wiener noises fractional noises and even jump noises in a forth coming paper using this new method we 46 prove the existence of random attractor for the stochastic nematic liquid crystals equations this is the first result about the long time behavior of stochastic nematic liquid crystals equations

well posedness of stochastic kdv bo equation driven by fractional brownian motion the cauchy problem for the korteweg de vries benjamin ono equation driven by cylindrical fractional brownian motion is discussed in this paper fractional brownian motion is a family of processes b h it is known that the smaller the value of hurst parameter h is the worse of the regularity of fbm is using bourgain restriction method we obtain the lower bound of the hurst parameter h for the driving processes b h with h 38 we prove local existence results with initial value in classical sobolev spaces of negative indices i e h s with s 18

existence uniqueness and stability of stochastic wave equation with cubic nonlinearities in two dimensions abstract the main focus of this article is the qualitative and quantitative behavior of stochastic wave equations with cubic nonlinearities in two dimensions we prove that the strong fourier solution of these semi linear wave equation exists and is unique on an appropriate hilbert space also we study the stability of solutions and give conclusions in three cases stability in probability estimates of l p growth and almost sure exponential stability the main tool is the study of related lyapunov type functionals which admits to control the total energy of randomly vibrating membranes the analysis is carried out by a natural n dimensional truncation in isometric hilbert spaces and uniform estimation of moments with respect to n

a decomposition approach to cpm it is shown that any continuous phase modulation cpm system can be decomposed into a continuous phase encoder and a memoryless modulator in such a way that the former is a linear modulo some integer p time invariant sequential circuit and the latter is also time invariant this decomposition is exploited to obtain alternative realizations of the continuous phase encoder and hence of cpm and also to obtain alternative forms of the optimum decoding algorithm when p is a prime p so that the encoder is linear over the finite field gf p it is shown that cascading it with an outside convolutional encoder is equivalent to a single convolutional encoder it is pointed out that the cascade of the modulator the waveform channel which it is assumed is characterized by additive white gaussian noise and the demodulator that operates over one symbol interval yield a discrete memoryless channel that can be studied without the distractions introduced by continuous phase encoding

multiple fractional integrals multiple integrals with respect to fractional brownian motion with h 1 2 are constructed for a large class of functions the first and second moments of the multiple integrals are explicitly identified

optimization of linear receivers for data communication signals the optimization of receivers constrained to consist of a linear filter and level slicer is considered for general data communication signals in additive white gaussian noise special consideration is given to the two limiting cases of arbitrarily low and high signal to noise ratios snrs the low snr case results in an average matched filter receiver the high snr filter is shown to be the solution to a specific nonlinear mathematical problem with a simple geometric interpretation an efficient algorithm is developed to solve the problem the results are illustrated for a duobinary minimum shift keyed signal observed over an interval of three symbol period duration

moment stability via resolvent operators of fractional stochastic differential inclusions driven by fractional brownian motion in this manuscript we consider a class of fractional stochastic differential inclusions driven by fractional brownian motion in hilbert space with hurst parameter h 12 1 sufficient conditions for the existence and asymptotic stability of mild solutions are derived in mean square moment by employing fractional calculus analytic resolvent operators and bohnenblustkarlins fixed point theorem the effectiveness of the obtained theoretical results is illustrated by an example

a class of quasilinear stochastic partial differential equations of mckean vlasov type with mass conservation a system ofn particles inr d with mean field interaction and diffusion is considered assuming adiabatic elimination of the momenta the positions satisfy a stochastic ordinary differential equation driven by brownian sheets microscopic equation where all coefficients depend on the position of the particles and on the empirical mass distribution process this empirical mass distribution process satisfies a quasilinear stochastic partial differential equation spde this spde mezoscopic equation is solved for general measure valued initial conditions by extending the empirical mass distribution process from point measure valued initial conditions with total mass conservation starting with measures with densities inl 2 r d dr wheredr is the lebesgue measure the solution will have densities inl 2 r d dr and strong uniqueness in the ito sense is obtained finally it is indicated how to obtain macroscopic partial differential equations as limits of the so constructed spde s

second order linear hyperbolic spdes driven by isotropic gaussian noise on a sphere we study a class of linear hyperbolic stochastic partial differential equations in bounded domains which includes the wave equation and the telegraph equation driven by gaussian noise that is white in time but not in space we give necessary and sufficient conditions on the spatial correlation of the noise for the existence and uniqueness of square integrable solutions in the particular case where the domain is a ball and the noise is concentrated on a sphere we characterize the isotropic gaussian noises with this property we also give explicit necessary and sufficient conditions when the domain is a hypercube and the gaussian noise is concentrated on a hyperplane

estimation de varadhan pour des diffusions a deux parametres sous des conditions de hormander generalisees la loi d une diffusion a parametre planaire possede une densite lisse en dehors des axes dans le cas elliptique nous etablissons une estimation de cette densite pur des petites valeurs du parametre celle ci constitue l analogue de l estimation de varadhan objet qui est bien connu dans le cas des diffusions ordinaires

gradient type noises ii systems of stochastic partial differential equations abstract the present paper is the second and main part of a study of partial differential equations under the influence of noisy perturbations existence and uniqueness of function solutions in the mild sense are obtained for a class of deterministic linear and semilinear parabolic boundary initial value problems if the noise data are random the results may be seen as a pathwise approach to spde s for typical examples such as spatially one dimensional stochastic heat equations with additive or multiplicative perturbations of fractional brownian type we recover and extend known results in addition we propose to consider partial noises of low order

macroscopic limits for stochastic partial differential equations of mckean vlasov type a class of quasilinear stochastic partial differential equations spdes driven by spatially correlated brownian noise is shown to become macroscopic i e deterministic as the length of the correlations tends to 0 the limit is the solution of a quasilinear partial differential equation the quasilinear spdes are obtained as a continuum limit from the empirical distribution of a large number of stochastic ordinary differential equations sodes coupled though a mean field interaction and driven by correlated brownian noise the limit theorems are obtained by application of a general result on the convergence of exchangeable systems of processes we also compare our approach to sodes with the one introduced by kunita

exact and approximate construction of digital phase modulations by superposition of amplitude modulated pulses amp minimum shift keying and offset qpsk are two well known modulations which can be interpreted as a set of time phase shifted am pulses we show in this paper that any constant amplitude binary phase modulation can also be expressed as a sum of a finite number of time limited amplitude modulated pulses amp decomposition new methods for computing autocorrelation and power frequency spectrum are derived which give very simple results for half integer index modulations we also show that the signal can be built with good accuracy using only one optimized pulse main pulse this synthesis is particularly satisfactory for modulations that have good spectral characteristics and or low index

symbol timing recovery for cpm with correlated data symbols we consider symbol timing recovery for continuous phase modulations cpms with correlated data symbols a popular example of such a scheme is shaped offset quadrature phase shift keying soqpsk we propose an extension to an existing non data aided blind timing error detector ted to make it compatible with such modulation schemes the merits of the modified ted are demonstrated by comparing its performance with and without taking the data correlation into account as a further modification we show that a quantization scheme can be used to yield an extremely low complexity version of the system with only negligible performance losses the s curve of the proposed quantized ted is given which rules out the existence of false lock points the proposed scheme shows great promise in a wide range of applications due to its low complexity its lack of false lock points and its blind nature such applications include timing recovery for noncoherent detection schemes and false lock detectors

a local time correspondence for stochastic partial differential equations it is frequently the case that a white noise driven parabolic and or hyperbolic stochastic partial differential equation spde can have random field solutions only in spatial dimension one here we show that in many cases where the spatial operator is the l generator of a levy process x a linear spde has a random field solution if and only if the symmetrization of x possesses local times this result gives a probabilistic reason for the lack of existence of random field solutions in dimensions strictly bigger than one in addition we prove that the solution to the spde is holder continuous in its spatial variable if and only if the said local time is holder continuous in its spatial variable we also produce examples where the random field solution exists but is almost surely unbounded in every open subset of space time our results are based on first establishing a quasi isometry between the linear l space of the weak solutions of a family of linear spdes on one hand and the dirichlet space generated by the symmetrization of x on the other hand we study mainly linear equations in order to present the local time correspondence at a modest technical level however some of our work has consequences for nonlinear spdes as well we demonstrate this assertion by studying a family of parabolic spdes that have additive nonlinearities for those equations we prove that if the linearized problem has a random field solution then so does the nonlinear spde moreover the solution to the linearized equation is holder continuous if and only if the solution to the nonlinear equation is and the solutions are bounded and unbounded together as well finally we prove that in the cases that the solutions are unbounded they almost surely blow up at exactly the same points date october 7 2007 2000 mathematics subject classification primary 60h15 60j55 secondary 35r60 35d05

comparison methods for a class of function valued stochastic partial differential equations a comparison theorem is derived for a class of function valued stochastic partial differential equations spde s with lipschitz coefficients driven by cylindrical and regular hilbert space valued brownian motions moreover we obtain necessary and sufficient conditions for the positivity of the mild solutions of the spde s where the sufficiency follows from the comparison theorem thereby it is e g possible to identify a class of spde s which can serve as stochastic space time models for the density of particles as a consequence we can construct unique mild solutions of spde s on the cone of positive functions with non lipschitz drift parts including the case of arbitrary polynomialsr x withr o o and leading negative coefficient

on the existence and position of the farthest peaks of a family of stochastic heat and wave equations we study the stochastic heat equation partial t u mathcal l u sigma u dot w in 1 1 dimensions where dot w is space time white noise r r is lipschitz continuous and mathcal l is the generator of a symmetric levy process that has finite exponential moments and u0 has exponential decay at we prove that under natural conditions on i the th absolute moment of the solution to our stochastic heat equation grows exponentially with time and ii the distances to the origin of the farthest high peaks of those moments grow exactly linearly with time very little else seems to be known about the location of the high peaks of the solution to the stochastic heat equation under the present setting see however gartner et al in probab theory relat fields 111 17 55 1998 gartner et al in ann probab 35 439 499 2007 for the analysis of the location of the peaks in a different model finally we show that these results extend to the stochastic wave equation driven by laplacian

uniqueness for stochastic non linear wave equations abstract we prove uniqueness of solutions of the equation u t t u f u g u w u 0 u 0 u t 0 v 0 on r d in the class of processes with paths in h 1 here u 0 v 0 is a random variable in h 1 l 2 w is a spatially homogeneous wiener process with finite spectral measure and f g are locally lipschitz functions of subcritical growth

regularity of gaussian processes on donne la validite de la conjecture de fernique 1974 sur l existence de mesures de majoration pouvant caracteriser la limitation des processus gaussiens

unstable invariant manifolds for stochastic pdes driven by a fractional brownian motion abstract in this paper we consider a class of stochastic partial differential equations spdes driven by a fractional brownian motion fbm with the hurst parameter bigger than 1 2 the existence of local random unstable manifolds is shown if the linear parts of these spdes are hyperbolic for this purpose we introduce a modified lyapunov perron transform which contains stochastic integrals by the singularities inside these integrals we obtain a special lyapunov perron s approach by treating a segment of the solution over time interval 0 1 as a starting point and setting up an infinite series equation involving these segments as time evolves using this approach we establish the existence of local random unstable manifolds in a tempered neighborhood of an equilibrium

on a jump type stochastic fractional partial differential equation with fractional noises abstract we study a class of stochastic fractional partial differential equations of order 1 driven by a pure jump levy space time white noise and a fractional noise we prove the existence and uniqueness of the global mild solution by the fixed point principle under some suitable assumptions

stochastic calculus with respect to gaussian processes in this paper we develop a stochastic calculus with respect to a gaussian process of the form b t int t 0 k t s dw s where w is a wiener process and k t s is a square integrable kernel using the techniques of the stochastic calculus of variations we deduce change of variable formulas for the indefinite integrals and we study the approximation by riemann sums the particular case of the fractional brownian motion is discussed

particle approximation of the wasserstein diffusion abstract we construct a system of interacting two sided bessel processes on the unit interval and show that the associated empirical measure process converges to the wasserstein diffusion von renesse and sturm 2009 25 assuming that markov uniqueness holds for the generating wasserstein dirichlet form the proof is based on the variational convergence of an associated sequence of dirichlet forms in the generalized mosco sense of kuwae and shioya 2003 19

absolute continuity of the law of the solution to the 3 dimensional stochastic wave equation abstract we present new results regarding the existence of density of the real valued solution to a 3 dimensional stochastic wave equation the noise is white in time and with a spatially homogeneous correlation whose spectral measure satisfies that r 3 d 1 2 for some 0 1 2 our approach is based on the mild formulation of the equation given by means of dalang s extended version of walsh s stochastic integration we use the tools of malliavin calculus let s 3 be the fundamental solution to the 3 dimensional wave equation the assumption on the noise yields upper and lower bounds for the integral 0 t ds r 3 d f s 3 s 2 and upper bounds for 0 t ds r 3 d f s 3 s 2 in terms of powers of t these estimates are crucial in the analysis of the malliavin variance which can be done by a comparison procedure with respect to smooth approximations of the distribution valued function s 3 t obtained by convolution with an approximation of the identity

pam decomposition of ternary cpm with duobinary encoding in this paper we investigate the pulse amplitude modulation pam decomposition and the spectral efficiency of duobinary continuous phase modulation cpm where duo binary cpm represents a ternary cpm whose symbols are generated using a duobinary encoder we show that this precoder ensures a higher spectral efficiency compared with binary cpm and we propose a pam decomposition characterized by the presence of a single main pulse and by uncorrelated pseudo symbols for a half integer modulation index value for this ternary cpm we show that shaped offset quadrature phase shift keying belongs to this cpm family and we provide a new reduced complexity trellis detector capable of reaching identical performance as the one introduced by perrins as well as new linear detectors

on the smoluchowski kramers approximation for a system with an infinite number of degrees of freedom according to the smolukowski kramers approximation we show that the solution of the semi linear stochastic damped wave equations utt t x u t x ut t x b x u t x qopen image in new window t u 0 u0 ut 0 v0 endowed with dirichlet boundary conditions converges as goes to zero to the solution of the semi linear stochastic heat equation ut t x u t x b x u t x qopen image in new window t u 0 u0 endowed with dirichlet boundary conditions moreover we consider relations between asymptotics for the heat and for the wave equation more precisely we show that in the gradient case the invariant measure of the heat equation coincides with the stationary distributions of the wave equation for any 0

global existence and explosion of the stochastic viscoelastic wave equation driven by multiplicative noises in this paper we discuss an initial boundary value problem of stochastic viscoelastic wave equation driven by multiplicative noise involving the nonlinear damping term utq 2ut and a source term of the type up 2u we first establish the local existence and uniqueness of solution by the iterative technique truncation function method moreover we also show that the solution is global for q p lastly by modifying the energy functional we give sufficient conditions such that the local solution of the stochastic equations will blow up with positive probability or explode in energy sense for p q

strong solutions to stochastic wave equations with values in riemannian manifolds let m be a d dimensional compact riemannian manifold we prove existence of a unique global strong solution of the stochastic wave equation dt tu dx xu yu tu xu w where y is a c1 smooth transformation and w is a spatially homogeneous wiener process on r whose spectral measure has finite moments up to order 2

on space time regularity for the stochastic heat equation on lie groups abstract we consider the stochastic heat equations on lie groups that is equations of the form t u x u b u f u w on r g where g is a compact lie group is the laplace beltrami operator on g b and f are lipschitz coefficients and where w is a gaussian space correlated noise which is white noise in time we find necessary and sufficient conditions on the space correlation of w such that u is an l 2 or holder continuous function in the spatial variable x using some basic tools of stochastic analysis and harmonic analysis on the lie group g

hydrodynamics in two dimensions and vortex theory we consider the navier stokes equation for a viscous and incompressible fluid inr2 we show that such an equation may be interpreted as a mean field equation vlasov like limit for a system of particles called vortices interacting via a logarithmic potential on which in addition a stochastic perturbation is acting more precisely we prove that the solutions of the navier stokes equation may be approximated in a suitable way by finite dimensional diffusion processes with the diffusion constant related to the viscosity as a particular case when the diffusion constant is zero the finite dimensional theory reduces to the usual deterministic vortex theory and the limiting equation reduces to the euler equation

mild solutions of the stochastic mhd equations driven by fractional brownian motions abstract the incompressible magnetohydrodynamic equations driven by additive fractional brownian motions are considered we firstly establish the local existence and uniqueness of the mild solution in l p space on a smooth bounded domain in r d d 2 3 the proof is based on the semigroup theory fixed point theorem and the results of stochastic pdes of linear parabolic type in the proof the eigenvalue problem with perfectly conducting wall condition is considered to weaken the requirements of noise terms finally the global existence of mild solutions is also established by energy estimate

the sharp markov property of levy sheets keywords brownian sheet two parameter levy processes sharp field poisson sheet splitting field reference prob article 1992 002doi 10 1214 aop 1176989793 record created on 2008 12 01 modified on 2017 05 12

on the stochastic heat equation with spatially colored random forcing we consider the stochastic heat equation of the following form t ut x lut x b ut x ut x t x for t 0 x r where l is the generator of a levy process and is a spatially colored temporally white gaussian noise we will be concerned mainly with the long term behavior of the mild solution to this stochastic pde for the most part we work under the assumptions that the initial data u0 is a bounded and measurable function and is nonconstant and lipschitz continuous in this case we find conditions under which the preceding stochastic pde admits a unique solution which is also weakly intermittent in addition we study the same equation in the case that lu is replaced by its massive dispersive analogue lu u where r and we describe accurately the effect of the parameter on the intermittence of the solution in the case that u is proportional to u the parabolic anderson model we also look at the linearized version of our stochastic pde that is the case when is identically equal to one any other constant works also in this case we study not only the existence and uniqueness of a solution but also the regularity of the solution when it exists and is unique

multiple bit differential detection of shaped offset qpsk we consider multiple bit differential detection mbdd of differentially encoded shaped offset quadrature phase shift keying soqpsk a highly bandwidth efficient and popular constant envelope modulation we propose two mbdd schemes that are based on a recent continuous phase modulation interpretation of soqpsk we show that the performance of these mbdd schemes approaches that of coherent detection cd as the multiple bit observation n window increases the first scheme uses a detection window that spans the full bit observation window f mbdd and is shown to require very large values of n to approach the performance of cd this presents a practical problem since the complexity of mbdd grows exponentially with n the second scheme is an improved version i mbdd with a detection window that is shortened to n 2 bit intervals although the complexity of i mbdd also increases exponentially with n it represents a significant improvement since only modest values of n are needed for high performance these performance characteristics are identified via a detailed performance analysis which provides asymptotic formulas for the bit error probability that are confirmed with computer simulations the analysis is also used to find the symmetric frequency pulse shapes with the best and worst error performance finally we develop a simplified and practical decision feedback differential detection algorithm that achieves near optimal performance with complexity that grows only linearly with n

a new performance bound for pam based cpm detectors it is well understood that the pulse amplitude modulation pam representation of continuous phase modulation cpm can lead to reduced complexity detectors with near optimum performance it has recently been shown that the pam representation also extends to cpm schemes with multiple modulation indexes multi h cpm in this paper we present a detector for multi h cpm which is based on the pam representation we also give an exact expression for the pairwise error probability for the entire class of pam based cpm detectors single and multi h optimal and reduced complexity over the additive white gaussian noise awgn channel and show that this bound is tighter than the previously published bound for approximate pam based detectors in arriving at this expression we show that pam based detectors for cpm are a special case of the broad class of mismatched cpm detectors we also show that the metrics for pam based detectors accumulate distance in a different manner than metrics for other cpm detectors these distance properties are especially useful in applications with greatly reduced trellis sizes we give thorough examples of the analysis for different single and multi h signaling schemes we also apply the new bound in comparing the performance of pam based detectors with other reduced complexity detectors for cpm

regularity of the sample paths of a class of second order spde s we study the sample path regularity of the solutions of a class of spde s which are second order in time and that includes the stochastic wave equation non integer powers of the spatial laplacian are allowed the driving noise is white in time and spatially homogeneous continuing with the work initiated in dalang and mueller 2003 we prove that the solutions belong to a fractional l 2 sobolev space we also

stochastic heat equation driven by fractional noise and local time the aim of this paper is to study the d dimensional stochastic heat equation with a multiplicative gaussian noise which is white in space and has the covariance of a fractional brownian motion with hurst parameter h 0 1 in time two types of equations are considered first we consider the equation in the ito skorohod sense and later in the stratonovich sense an explicit chaos expansion for the solution is obtained on the other hand the moments of the solution are expressed in terms of the exponential moments of some weighted intersection local time of the brownian motion

the finite speed of propagation for solutions to nonlinear stochastic wave equations driven by multiplicative noise abstract we prove that the solutions to the stochastic wave equation in o r d d x x d t g x d t x d w for 1 d where g is a continuous function with polynomial growth of order less or equal to d d 2 and is lipschitz with 0 0 propagate with finite speed this result resembles the classical finite speed of propagation result for the solution to the klein gordon equation and extends to equations with dissipative damping a similar result follows for the equation with additive noise of the form f t d w where f t f t has compact support in for each t 0

decision feedback detectors for soqpsk we consider highly simplified decision feedback detectors for shaped offset quadrature phase shift keying soqpsk a highly bandwidth efficient and popular constant envelope modulation in particular we show that the state complexity can be reduced to a minimal level two states with asymptotically optimum performance as demonstrated by performance analysis and confirmed by computer simulations the complexity reduction is achieved by a novel manipulation of the differential encoder and the soqpsk precoder which are both part of the transmission model for soqpsk we give two possible architectures for achieving this complexity reduction the pulse amplitude modulation pam technique and the pulse truncation pt technique we also formulate these detectors for coherent and noncoherent detection the resulting family of detectors makes use of recent advances in soqpsk technology based on a continuous phase modulation cpm interpretation of soqpsk the proposed simplifications are significant because they minimize the complexity of trellis based soqpsk detectors which have become available only in recent years because trellis based soqpsk detectors are 1 2 db superior to the widely deployed family of symbol by symbol soqpsk detectors the proposed two state detectors offer the simplest means of achieving these performance gains thus these simple detection schemes are applicable in settings where high performance and low complexity are needed to meet restrictions on power consumption and cost

mean field backward stochastic differential equations a limit approach mathematical mean field approaches play an important role in different fields of physics and chemistry but have found in recent works also their application in economics finance and game theory the objective of our paper is to investigate a special mean field problem in a purely stochastic approach for the solution y z of a mean field backward stochastic differential equation driven by a forward stochastic differential of mckean vlasov type with solution x we study a special approximation by the solution x n y n z n of some decoupled forward backward equation which coefficients are governed by n independent copies of x n y n z n we show that the convergence speed of this approximation is of order 1 root n moreover our special choice of the approximation allows to characterize the limit behavior of root n x n x y n y z n z we prove that this triplet converges in law to the solution of some forward backward stochastic differential equation of mean field type which is not only governed by a brownian motion but also by an independent gaussian field

the existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional brownian motion abstract in this paper we investigate the existence uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed by a fractional brownian motion b q h t d x t a x t f t x t d t g t d b q h t with hurst parameter h 1 2 1 we also consider the existence of weak solutions

time space fractional stochastic ginzburg landau equation driven by fractional brownian motion abstract the current paper is devoted to the time space fractional ginzburg landau equation driven by fractional brownian motion the spatial temporal regularity of the nonlocal stochastic convolution is firstly established and then the existence and uniqueness of the global mild solution are obtained by the banach fixed point theorem and mittag leffler functions finally the numerical simulations for the time fractional stochastic ginzburg landau equation are provided to verify the mathematical analysis results

nonlinear stochastic wave and heat equations we study nonlinear wave and heat equations on d driven by a spatially homogeneous wiener process for the wave equation we consider the cases of d 1 2 3 the heat equation is considered on an arbitrary d space we give necessary and sufficient conditions for the existence of a function valued solution in terms of the covariance kernel of the noise

intermittency for the wave and heat equations with fractional noise in time in this article we consider the stochastic wave and heat equations driven by a gaussian noise which is spatially homogeneous and behaves in time like a fractional brownian motion with hurst index h 1 2 the solutions of these equations are interpreted in the skorohod sense using malliavin calculus techniques we obtain an upper bound for the moments of order p 2 of the solution in the case of the wave equation we derive a feynman kac type formula for the second moment of the solution based on the points of a planar poisson process this is an extension of the formula given by dalang mueller and tribe trans amer math soc 360 2008 4681 4703 in the case h 1 2 and allows us to obtain a lower bound for the second moment of the solution these results suggest that the moments of the solution grow much faster in the case of the fractional noise in time than in the case of the white noise in time

a class of reduced complexity viterbi detectors for partial response continuous phase modulation partial response continuous phase modulation cpm gives constant envelope digital modulation schemes with excellent power spectra both narrow main lobe and low spectral tails can be achieved when these signals are detected in an optimum coherent maximum likelihood sequence detector viterbi detector power efficient schemes can also be designed sometimes at the expense of receiver complexity this paper describes a general class of simple viterbi detectors with reduced complexity compared to the optimum case the key idea is that the approximate receiver is based on a less complex cpm scheme than the transmitted scheme the asymptotically optimum reduced complexity receiver is found for a variety of transmitted schemes and various complexity reduction factors for a specific class of receivers and modulation indexes a new distance measure is introduced for the performance analysis smooth schemes based on raised cosine pulses are analyzed and simulated for the case of simplified reception a graceful performance degradation occurs with the reduction of complexity

reduced complexity approach to iterative detection of coded soqpsk we develop a reduced complexity approach for the detection of coded shaped offset quadrature phase shift keying soqpsk a highly bandwidth efficient and popular constant envelope modulation the complexity savings result from viewing the signal as a continuous phase modulation cpm we give a simple and convenient closed form expression for a recursive binary to ternary precoder for soqpsk the recursive nature of this formulation is necessary in serially concatenated systems where soqpsk serves as the inner code we show that the proposed detectors are optimal in the full response case and are near optimal in the partial response case due to some additional complexity reducing approximations in all cases the proposed detectors achieve large coding gains for serially concatenated coded soqpsk these gains are similar to those reported recently by li and simon which were obtained using a more complicated cross correlated trellis coded quadrature modulation xtcqm interpretation

laurent s representation of binary digital continuous phase modulated signals with modulation index 1 2 revisited in order to simplify modulator and demodulator structures the composition of binary continuous phase modulations cpms by the linear superposition of impulses as developed by laurent 1986 is advantageous based on differential encoding of the binary data sequence a novel cpm modulator concept for modulation index 1 2 is presented

a high performance reduced complexity gmsk demodulator a four state adaptive maximum likelihood sequence estimation mlse gaussian minimum shift keying gmsk demodulator for modulation bt 0 3 on awgn channels is analyzed and simulated this demodulator uses the linear representation of gmsk signals and achieves near optimum ber performance the channel impulse response used in the mlse demodulator is initialized to the highest energy component in the linear representation and then adapted in a decision directed mode to offset any performance losses incurred by initially ignoring other lower energy and time varying components in the linear representation the number of mlse states is reduced to two at about 0 1 db performance loss by implementing a whitening matched filter which concentrates most of the gmsk pulse energy in its two leading samples

sharp gaussian regularity on the circle and applications to the fractional stochastic heat equation abstract a sharp regularity theory is established for homogeneous gaussian fields on the unit circle two types of characterizations for such a field to have a given almost sure uniform modulus of continuity are established in a general setting the first characterization relates the modulus to the field s canonical metric the full force of fernique s zero one laws and talagrand s theory of majorizing measures is required the second characterization ties the modulus to the field s random fourier series representation as an application it is shown that the fractional stochastic heat equation has up to a non random constant a given spatial modulus of continuity if and only if the same property holds for a fractional antiderivative of the equation s additive noise a random fourier series characterization is also given

a stochastic wave equation in two space dimension smoothness of the law we prove the existence and uniqueness for any time of a real valued process solving a nonlinear stochastic wave equation driven by a gaussian noise white in time and correlated in the two dimensional space variable we prove that the solution is regular in the sense of the malliavin calculus we also give a decay condition on the covariance function of the noise under which the solution has holder continuous trajectories a d show that under an additional ellipticity assumption the law of the solution at any strictly positive time has a smooth density

random nonlinear wave equations propagation of singularities on etudie les proprietes de lissite des solutions d equations d ondes unidimensionnelles avec forcing aleatoire non lineaire on definit les singularites comme anomalies dans le modulo local de continuite des solutions

long time existence for the wave equation with a noise term we consider the equationut uxx u w forx on a finite interval with dirichlet boundary conditions w is spacetime white noise the initial condition is continuous and nonnegative we show existence and uniqueness for all time provided 1 3 2

chaos decomposition of multiple fractional integrals and applications chaos decomposition of multiple integrals with respect to fractional brownian motion with h 1 2 is given conversely the chaos components are expressed in terms of the multiple fractional integrals tensor product integrals are introduced and series expansions in those are considered strong laws for fractional brownian motion are proved as an application of multiple fractional integrals

stochastic wave equation with critical nonlinearities temporal regularity and uniqueness we consider a nonlinear wave equation utt u f u g u w on r d driven by a spatially homogeneous wiener process w with a finite spectral measure and with nonlinear terms f g of critical growth we study pathwise uniqueness and norm continuity of paths of u ut in h 1 rd l2 rd under the hypothesis that there exists a local solution u such that u ut has weakly continuous paths in h 1

stochastic evolution equations with fractional brownian motion in this paper linear stochastic evolution equations driven by infinite dimensional fractional brownian motion are studied a necessary and sufficient condition for the existence and uniqueness of the solution is established and the spatial regularity of the solution is analyzed separate proofs are required for the cases of hurst parameter above and below 1 2 the particular case of the laplacian on the circle is discussed in detail

evolution equation of a stochastic semigroup with white noise drift we study the existence and uniqueness of the solution of a functionvalued stochastic evolution equation based on a stochastic semigroup whose kernel p s t y x is brownian in s and t the kernel p is supposed to be measurable with respect to the increments of an underlying wiener process in the interval s t the evolution equation is then anticipative and choosing the skorohod formulation we establish existence and uniqueness of a continuous solution with values in l r as an application we prove the existence of a mild solution of the stochastic parabolic equation dut xudt v dt x ru f t x u w dt x where v and w are brownian in time with respect to a common ltration in this case p is the formal backward heat kernel of x v dt x rx supported by the dgicyt grant no pb96 0087 ysupported by nsf international opportunities postdoctoral fellowship no int9600278 and nsf nato postdoctoral fellowship no dge 9633937 ams subject classi cation primary 60h15 secondary 60h07

stochastic averaging for a class of two time scale systems of stochastic partial differential equations abstract this paper focuses on systems of stochastic partial differential equations that have a slow component driven by a fractional brownian motion and a fast component driven by a fast varying diffusion we establish an averaging principle in which the fast varying diffusion process acts as a noise and is averaged out in the limit the slow process is shown to have a limit in the l 2 sense which is characterized by the solution of a stochastic partial differential equation driven by a fractional brownian motion whose coefficients are averages of that of the original slow process with respect to the stationary measure of the fast varying diffusion this averaging principle paves a way for reduction of computational complexity the implication is that one can ignore the complex original systems and concentrate on the average systems instead

noise sharing and mexican hat coupling in a stochastic neural field a diffusion type coupling operator that is biologically significant in neuroscience is a difference of gaussian functions mexican hat operator used as a spatial convolution kernel we are interested in pattern formation by stochastic neural field equations a class of space time stochastic differential integral equations using the mexican hat kernel we explore quantitatively how the parameters that control the shape of the coupling kernel the coupling strength and aspects of spatially smoothed space time noise influence the pattern in the resulting evolving random field we confirm that a spatial pattern that is damped in time in a deterministic system may be sustained and amplified by stochasticity we find that spatially smoothed noise alone causes pattern formation even without direct spatial coupling our analysis of the interaction between coupling and noise sharing allows us to determine parameter combinations that are optimal for the formation of spatial pattern

pam representation of ternary cpm this letter considers the pulse amplitude modulation pam representation of continuous phase modulation cpm with a ternary data alphabet this technique is applied to the problem of constructing reduced complexity detectors with near optimum performance the usefulness of this approach is demonstrated using the ternary cpm variant known as shaped offset quadrature phase shift keying soqpsk

makespan minimization on unrelated parallel machines with simple job intersection structure and bounded job assignments abstract let there be a set j of n jobs and a set m of m parallel machines where each job j j takes p i j z time units on machine m i and assume p i j implies job j j cannot be scheduled on machine m i in makespan minimization on unrelated parallel machines r c m a x the goal is to schedule each job non preemptively on a machine so as to minimize the makespan a job intersection graph g j j e j is an unweighted undirected graph where there is an edge j j j j e j if there is a machine m i such that both p i j and p i j in this paper we consider two variants of r c m a x where there are a small number of eligible jobs per machine first we prove that there are no approximation algorithms with approximation ratios less than 3 2 for r c m a x when restricted to instances with job intersection graphs belonging to some graph classes such as diamondless graphs and planar graphs unless p np second we match this lower bound by presenting a 3 2 approximation algorithm for r c m a x restricted to instances with diamondless job intersection graphs and furthermore show that when g j is triangle free r c m a x is solvable in polynomial time for r c m a x restricted to instances when every machine can process at most l jobs we give an approximation algorithm with approximation ratios 3 2 and 5 3 for l 3 and l 4 respectively a polynomial time algorithm when l 2 and prove that it is np hard to approximate the optimum solution within a factor less than 3 2 when l 3 in the special case where every p i j p j called the restricted assignment problem and there are only two job lengths p j we present a 2 1 l 1 approximation algorithm when l 3 in addition we give a 2 approximation algorithm for the so called unrelated graph balancing problem for l 3 in the case where j is partitioned into b sets called bags and no two jobs from the same bag can be scheduled on the same machine

a note on stochastic schrodinger equations with fractional multiplicative noise abstract this work is devoted to non linear stochastic schrodinger equations with multiplicative fractional noise where the stochastic integral is defined following the riemann stieljes approach of zahle under the assumptions that the initial condition is in the sobolev space h q r n for a dimension n less than three and q an integer greater than or equal to zero that the noise is a q fractional brownian motion with hurst index h 1 2 1 and spatial regularity h q 4 r n as well as appropriate hypotheses on the non linearity we obtain the local existence of a unique pathwise solution in c 0 0 t h q r n c 0 0 t h q 2 r n for any 0 h contrary to the parabolic case standard fixed point techniques based on the mild formulation of the spde cannot be directly used because of the weak smoothing in time properties of the schrodinger semigroup we follow here a different route and our proof relies on a change of phase that removes the noise and leads to a schrodinger equation with a magnetic potential that is not differentiable in time

properties of the density for a three dimensional stochastic wave equation abstract we consider a stochastic wave equation in space dimension three driven by a noise white in time and with an absolutely continuous correlation measure given by the product of a smooth function and a riesz kernel let p t x y be the density of the law of the solution u t x of such an equation at points t x 0 t r 3 we prove that the mapping t x p t x y owns the same regularity as the sample paths of the process u t x t x 0 t r 3 established in r c dalang m sanz sole holder sobolev regularity of the solution to the stochastic wave equation in dimension three mem amer math soc in press the proof relies on malliavin calculus and more explicitly the integration by parts formula of s watanabe lectures on stochastic differential equations and malliavin calculus tata inst fund res springer verlag bombay 1984 and estimates derived from it

a feynman kac type formula for the deterministic and stochastic wave equations and other p d e s we establish a probabilistic representation for a wide class of linear deterministic p d e s with potential term including the wave equation in spatial dimensions 1 to 3 our representation applies to the heat equation where it is related to the classical feynman kac formula as well as to the telegraph and beam equations if the potential is a random spatially homogeneous gaussian noise then this formula leads to an expression for the moments of the solution