an affine invariant bivariate version of the sign test abstract the generalized median of h oja yields a notion of bivariate quantile and in turn an affine invariant bivariate analogue of the sign test its properties include a simple null covariance formula facilitating a permutation or sign change test in the case of bivariate symmetry normal efficiency coinciding with that of the oja median and bounded influence hence strong robustness author

impacts of noise on a class of partial differential equations abstract this paper is concerned with effects of noise on the solutions of partial differential equations we first provide a sufficient condition to ensure the existence of a unique positive solution for a class of stochastic partial differential equations then we prove that noise could induce singularities finite time blow up of solutions finally we show that a stochastic allen cahn equation does not have finite time singularities and the unique solution exists globally

local unstable manifolds of periodic orbits in thin domains abstract we compare the dynamics of a system of damped wave equations on a thin domain with the dynamics of the limit system when the thickness of the thin domain goes to 0 more precisely under the assumption that the problem in the thin domain admits a periodic orbit e close to a hyperbolic periodic orbit 0 of the problem in the limit domain we show that e is also hyperbolic and that the local unstable manifold of the periodic orbit e is close to the local unstable manifold of 0

continuous dependence on the coefficients and global existence for stochastic reaction diffusion equations abstract we prove convergence of the solutions x n of semilinear stochastic evolution equations on a banach space b driven by a cylindrical brownian motion in a hilbert space h d x n t a n x t f n t x n t d t g n t x n t d w h t x n 0 n assuming that the operators a n converge to a and the locally lipschitz functions f n and g n converge to the locally lipschitz functions f and g in an appropriate sense moreover we obtain estimates for the lifetime of the solution x of the limiting problem in terms of the lifetimes of the approximating solutions x n we apply the results to prove global existence for reaction diffusion equations with multiplicative noise and a polynomially bounded reaction term satisfying suitable dissipativity conditions the operator governing the linear part of the equation can be an arbitrary uniformly elliptic second order elliptic operator

ornstein uhlenbeck processes with singular drifts integral estimates and girsanov densities we consider a perturbation of a hilbert space valued ornstein uhlenbeck process by a class of singular nonlinear non autonomous maximal monotone time dependent drifts the only further assumption on the drift is that it is bounded on balls in the hilbert space uniformly in time first we introduce a new notion of generalized solutions for such equations which we call pseudo weak solutions and prove that they always exist and obtain pathwise estimates in terms of the data of the equation then we prove that their laws are absolutely continuous with respect to the law of the original ornstein uhlenbeck process in particular we show that pseudo weak solutions always have continuous sample paths in addition we obtain integrability estimates of the associated girsanov densities some of our results concern non random equations as well while probabilistic results are new even in finite dimensional autonomous settings

existence uniqueness and continuous dependence for implicit semilinear functional differential equations abstract theorems of existence uniqueness and continuous dependence for the nonlinear functional differential equation d d t au t bu t f t u t in a banach space are proved the unbounded operator a is generally degenerate abstract results are applied to nonlinear partial functional differential equations in particular a model of liquid filtration in fissured porous rocks is considered

detecting unequal marginal scales in a bivariate population abstract a conditional test is proposed that uses the null hypothesis of bivariate symmetry to detect unequal marginal scales in a bivariate population the asymptotic normality of the test statistic and the consistency of the test are established asymptotic relative efficiency comparisons are made with the standard parametric test in both the bivariate normal case and in a trivariate reduction model case and with two of sen s 1967 tests in the bivariate normal case the good performance of the test is also illustrated via a monte carlo study

ergodicity of stochastic 2d navier stokes equation with levy noise abstract in this paper we deal with the 2d navier stokes equation perturbed by a levy noise force whose white noise part is non degenerate and that the intensity measure of poisson measure is finite existence and uniqueness of invariant measure for this equation is obtained two main properties of the markov semigroup associated with this equation are proved in other words strong feller property and irreducibility hold in the same space

irreducibility and exponential mixing of some stochastic hydrodynamical systems driven by pure jump noise in this paper we derive several results related to the long time behavior of a class of stochastic semilinear evolution equations in a separable hilbert space h d mathfrak u t rm a mathfrak u t rm b mathfrak u t mathfrak u t dt dl t quad mathfrak u 0 x in rm h here a is a positive self adjoint operator and b is a bilinear map and the driving noise l is basically a d rm a 1 2 valued levy process satisfying several technical assumptions by using a density transformation theorem type for levy measure we first prove a support theorem and an irreducibility property of the ornstein uhlenbeck processes associated to the nonlinear stochastic problem second by exploiting the previous results we establish the irreducibility of the nonlinear problem provided that for a certain gamma in 0 1 4 b is continuous on d rm a gamma times d rm a gamma with values in d rm a 1 2 using a coupling argument the exponential ergodicity is also proved under the stronger assumption that b is continuous on rm h times rm h while the latter condition is only satisfied by the nonlinearities of goy and sabra shell models the assumption under which the irreducibility property holds is verified by several hydrodynamical systems such as the 2d navier stokes magnetohydrodynamics equations the 3d leray varvec alpha model the goy and sabra shell models

one dimensional stochastic burgers equation driven by levy processes abstract in this paper we proved the global existence and uniqueness of the strong weak and mild solutions for one dimensional burgers equation perturbed by a poisson form process a poisson form and q wiener process with the dirichlet bounded condition we also proved the existence of the invariant measure of these models

an efficient code timing estimator for ds cdma signals we present an efficient algorithm for estimating the code timing of a known training sequence in an asynchronous direct sequence code division multiple access ds cdma system the algorithm is a large sample maximum likelihood lsml estimator that is derived by modeling the known training sequence as the desired signal and all other signals including the interfering signals and thermal noise as unknown colored gaussian noise that is uncorrelated with the desired signal the lsml estimator is shown to be robust against the near far problem and is also compared with several other code timing estimators via numerical examples it is found that the lsml approach can offer noticeable performance improvement especially when the loading of the system is heavy

finite sample properties and asymptotic efficiency of monte carlo tests on donne une approche unifiee qui couvre le cas d une distribution nulle arbitraire afin d etudier les proprietes statistiques des tests de monte carlo

global existence and stability of solutions for reaction diffusion functional differential equations in this article a class of reaction diffusion functional differential equations is investigated the global existence and uniqueness of solutions and the stability of the trivial solution are obtained some applications are also discussed the method proposed in this article is a combination of the iterative analysis the fixed point theorem and the comparison principle

stochastic functional partial differential equations existence uniqueness and asymptotic decay property existence and uniqueness of strong solutions for a class of stochastic functional differential equations in hilbert spaces are established sufficient conditions which guarantee the transference of mean square and pathwise exponential stability from stochastic partial differential equations to stochastic functional partial differential equations are studied the stability results derived are also applied to stochastic ordinary differential equations with hereditary characteristics in particular as a direct consequence our main results improve some of those by mao shah in which it was proved that under certain conditions pathwise exponential stability is transferred from non delay equations to delay equations if the constant time lag appearing in the problem is sufficiently small while in our treatment the transference actually holds for arbitrary bounded delay variables not only in finite but in infinite dimensions

spdes driven by poisson random measure with non lipschitz coefficients existence results the article deals with spdes driven by poisson random measure with non lipschitz coefficients let a e e be a generator of an analytic semigroup on e e being a certain banach space let open image in new window be a stochastic basis carrying an e valued poisson random measure with characteristic measure and compensator let 1 p 2 our point of interest is the existence of solutions to spde s of e g the following type

bifurcation and multiplicity results for periodic solutions of a damped wave equation in a thin domain we study the bifurcation problem for periodic solutions of a nonautonomous damped wave equation dened in a thin domain here the bifurcation parameter is represented by the thinness 0 of the considered domain this study has as starting point the existence result of periodic solutions already stated by the authors for this equation and it makes use of the condensivity properties of the associated poincare map and its linearization around these solutions we establish sucient conditions to guarantee that 0 is or not a bifurcation point and a related multiplicity result these results are in the spirit of those given by krasnosel skii and they are obtained by using the topological degree theory for k condensing operators c 2000 elsevier science b v all rights reserved

on parameter estimation in long code ds cdma systems cramer rao bounds and least squares algorithms the problem of parameter estimation in direct sequence code division multiple access ds cdma systems employing long aperiodic spreading codes is considered in particular for an asynchronous network the problem of estimating the amplitudes phase offsets propagation delays and directions of arrival doas for the cdma signals transmitted by the active users is examined first formulas are provided for the cramer rao bound crb on the error variance of any joint multiuser parameter estimation procedure exploiting a known training sequence further least squares adaptive algorithms are derived which based on the transmission of known pilot symbols enable adaptive estimation of the parameters with a computational complexity that is only quadratic in the processing gain in particular the cases where either the parameters from all of the active users are to be estimated or the relevant parameters of only one user are to be acquired based on the knowledge of its spreading code and training sequence only are considered this study is completed by an analysis of the convergence properties of the proposed adaptive algorithms and by extensive computer simulation results illustrating the performance of the estimation procedures also in comparison with the crb and the impact of the estimation errors on the performance of the linear minimum mean square error lmmse multiuser detector

optimal local holder index for density states of superprocesses with 1 β branching mechanism for 0 0 if d 1 but locally unbounded otherwise moreover in the case of continuity we determine the optimal local holder index

on the probability density function of the lms adaptive filter weights the joint probability density function of the weight vector in least mean square lms adaptation is studied for gaussian data models an exact expression is derived for the characteristic function of the weight vector at time n 1 conditioned on the weight vector at time n the conditional characteristic function is expanded in a taylor series and averaged over the unknown weight density to yield a first order partial differential difference equation in the unconditioned characteristic function of the weight vector the equation is approximately solved for small values of the adaption parameter and the weights are shown to be jointly gaussian with time varying mean vector and covariance matrix given as the solution to well known difference equations for the weight vector mean and covariance matrix the theoretical results are applied to analyzing the use of the weights in detection and time delay estimation simulations that support the theoretical results are also presented

long time existence for the heat equation with a noise term we consider the equationu t u xx 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

existence uniqueness and asymptotic behavior of mild solutions to stochastic functional differential equations in hilbert spaces abstract in this paper we shall consider the existence uniqueness and asymptotic behavior of mild solutions to stochastic partial functional differential equations with finite delay r 0 dx t ax t f t x t dt g t x t dw t where we assume that a is a closed densely defined linear operator and the generator of a certain analytic semigroup f c h g c l 0 2 k h are two locally lipschitz continuous functions where c c r 0 d a l 0 2 k h are two proper infinite dimensional spaces 0 w t is a given k valued wiener process and both h and k are separable hilbert spaces

a novel adaptive antenna array for ds cdma code acquisition equipped with an adaptive beamformer existing adaptive array code acquisition still relies on the correlator structure due to the inherent property of the associated serial search scheme its mean acquisition time is large especially in strong interference environments in this paper we propose a novel adaptive filtering scheme to solve the problem the proposed scheme comprises two adaptive filters an adaptive spatial and an adaptive temporal filter with a specially designed structure the spatial filter can act as a beamformer suppressing interference while the temporal filter can act as a code delay estimator a mean squared error mse criterion is proposed such that these filters can be simultaneously adjusted by a stochastic gradient descent method the performance as well as the convergence behavior of the proposed algorithm are analyzed in detail closed form expressions for optimum filter weights optimum beamformer signal to interference plus noise ratio sinr steady state mse and mean acquisition time are derived for the additive white gaussian noise awgn channel computer simulations show that the mean acquisition time of the proposed algorithm is much shorter than that of the correlator based approach and the derived theoretical expressions are accurate

an efficient code timing estimator for receiver diversity ds cdma systems we propose an efficient algorithm for estimating the code timing of direct sequence code division multiple access ds cdma systems that consist of an arbitrary antenna array at the receiver and work in a flat fading and near far environment the algorithm is an asymptotic for large number of data samples maximum likelihood ml estimator that is derived by modeling the known training sequence as the desired signal and all other signals including the interfering signals and the additive noise as unknown colored gaussian noise the algorithm does not require the search over a parameter space and the code timing is obtained by rooting a second order polynomial which is computationally very efficient simulation results show that the algorithm is quite robust against the near far problem and channel fading it requires a shorter training sequence than the single antenna based estimators

optimal control of semilinear stochastic evolution equations the aim of this paper is to initiate a semigroup theory based approach to characterization of optimal markov controls for controlled semilinear stochastic evolution equations it may be recalled that markov controls are those that depend only on the current state at each time for finite dimensional controlled stochastic differential equations with a nondegenerate diffusion matrix this task is traditionally achieved through the hamilton jacobi bellman equation of dynamic programming associated with the problem and an accompanying verification theorem the latter states that an optimal markov control can be explicitly obtained by the pointwise minimization of a hamiltonian derivable from the solution of the hjb equation moreover any optimal markov control is obtainable in this manner

a class of permutation tests of bivariate interchangeability abstract a set of permutation tests that are both exact and distribution free are proposed to simultaneously detect differences in marginal locations and or scales in bivariate data the tests take advantage of the fact that when the marginal means and variances are equal the pairwise differences are symmetrically distributed about 0 and are uncorrelated with the pairwise sums two statistics for detecting the marginal location and scale differences are combined in a quadratic form a permutation distribution for this quadratic form follows from considering all 2 n conditionally equally likely sign changes on the differences several methods of estimating the covariance matrix of the quadratic form are examined including conditional and unconditional plug in approaches these new tests are compared with the standard tests in the literature and through simulation for several families of bivariate distributions are found to compare quite favorably this article also brings to light the largely overloo

gradient estimates for sdes driven by multiplicative levy noise abstract gradient estimates are derived for the first time for the semigroup associated to a class of stochastic differential equations driven by multiplicative levy noise in particular the estimates are sharp for stable type noises to derive these estimates a new derivative formula of bismut elworthy li s type is established for the semigroup by using the malliavin calculus and a finite jump approximation argument

stochastic partial differential equation driven by stable noise we construct a weak solution to the stochastic partial differential equation driven by a one sided stable noise without negative jumps we prove the weak existence of the solution for parameters the facts that for is not a lipschitz function and is not a gaussian noise require the development of new methods which we believe are of independent interest we also show that when the above equation gives an alternative description of super brownian motion with stable branching mechanism

local martingale solutions to the stochastic two layer shallow water equations with multiplicative white noise abstract we study the two layers shallow water equations on a bounded domain m r 2 driven by a multiplicative white noise and obtain the existence and uniqueness of a maximal pathwise solution for a limited period of time the time of existence being strictly positive almost surely the proof makes use of anisotropic estimates and stopping time arguments of the skorohod representation theorem and the gyongy krylov theorem which is an infinite dimensional analogue of the yamada watanabe theorem

oscillations of solutions of vector differential equations of parabolic type with functional arguments vector parabolic differential equations with functional arguments are studied and the oscillations of solutions of boundary value problems are investigated our approach is to reduce the oscillation problems to the nonexistence of positive solutions of scalar differential inequalities by employing the concept of h oscillation introduced by domslak see r courant d hilbert methods of mathematical physics vol i interscience new york 1996 where h denotes a unit vector

the existence and asymptotic behaviour of energy solutions to stochastic 2d functional navier stokes equations driven by levy processes abstract let d be a bounded or unbounded open domain of 2 dimensional euclidean space r 2 if the boundary d exists then we assume that the boundary is smooth in this paper assuming that the kinematic viscosity 0 is large enough we discuss the existence and exponential stability of energy solutions to the following 2 dimensional stochastic functional navier stokes equation perturbed by the levy process d x t x t x t x t f t x t f t x t p d t d x t g t x t d w t u k t x t y q d t d y d i v x 0 in 0 d where x t x t x is the initial function for x d and t r 0 with r 0 it is assumed that f g f and k satisfy the lipschitz condition and the linear growth condition if there exists the boundary d then x t x 0 on 0 d

lower estimates of transition densities and bounds on exponential ergodicity for stochastic pde s a formula for the transition density of a markov process defined by an infinite dimensional stochastic equation is given in terms of the ornstein uhlenbeck bridge and a useful lower estimate on the density is provided as a consequence uniform exponential ergodicity and v ergodicity are proved for a large class of equations we also provide computable bounds on the convergence rates and the spectral gap for the markov semigroups defined by the equations the bounds turn out to be uniform with respect to a large family of nonlinear drift coefficients examples of finite dimensional stochastic equations and semilinear parabolic equations are given

on the abstract cauchy problem of parabolic type in spaces of continuous functions on etudie l existence l unicite et les proprietes de regularite des solutions du probleme de cauchy u t au r f t o t t u o u 0 ou a d a ce e est un operateur lineaire clos dans l espace de banach e

exponential mixing properties of stochastic pdes through asymptotic coupling we consider parabolic stochastic partial differential equations driven by white noise in time we prove exponential convergence of the transition probabilities towards a unique invariant measure under suitable conditions these conditions amount essentially to the fact that the equation transmits the noise to all its determining modes several examples are investigated including some where the noise does not act on every determining mode directly

necessary conditions for partial differential equations with delay to generate c0 semigroups on etudie l existence des solutions ou le caractere bien pose d equations aux derivees partielles a retard du type du t dt f u t ou f est un operateur d un espace de fonction 7b f r 0 y dans l espace de banach y dans lequel l equation evolue

explosive solutions of stochastic reaction diffusion equations in mean lp norm abstract the paper is concerned with the problem of non existence of global solutions for a class of stochastic reaction diffusion equations of ito type under some sufficient conditions on the initial state the nonlinear term and the multiplicative noise it is proven that in a bounded domain d r d there exist positive solutions whose mean l p norm will blow up in finite time for p 1 while if d r d the previous result holds in any compact subset of r d two examples are given to illustrate some application of the theorems

random perturbations of reaction diffusion equations the quasi deterministic approximation on considere des champs aleatoires u e t x u 1 e t x u n e t x definis comme les solutions d un systeme d equations aux derivees partielles u k e t l k u k e f k x u 1 e u n e e k t x les l k sont des operateurs elliptiques lineaires d ordre 2 k sont des champs gaussiens bruit blanc

a family of distributions for modelling non elliptically symmetric multivariate data summary the paucity of distributions that can be used as an aid to modelling the structure of multivariate data is a recognized limitation we present a relatively simple family of distributions for use in describing data which are not elliptically symmetric properties of the family are discussed and it is shown that multivariate pareto burr and logistic distributions are special cases in addition simulation methods for applications in monte carlo robustness studies are outlined and finally the fit to a data set on uranium exploration is compared to that obtained using the usual bivariate normal distribution

non explosion boundedness and ergodicity for stochastic semilinear equations abstract sufficient conditions for non explosion boundedness and ergodicity of solutions of a class of semilinear stochastic equations are given applications of the results are based on a new regularity theorem for solutions of the linear problem

convergence to equilibrium for classical and quantum spin systems the paper is devoted to stochastic equations describing the evolution of classical and quantum unbounded spin systems on discrete lattices and on euclidean spaces existence and asymptotic properties of the corresponding transition semigroups are studied in a unified way using the theory of dissipative operators on weighted hilbert and banach spaces this paper is an enlarged and rewritten version of the paper 7

blow up of solutions for semilinear stochastic delayed reaction diffusion equations with levy noise abstract this paper is concerned with a class of semilinear stochastic delayed reaction diffusion equations driven by levy noise in a separable hilbert space we establish sufficient conditions to ensure the existence of a unique positive solution moreover we study blow up of solutions in finite time in mean l p norm sense several examples are given to illustrate applications of the theory

blowup for the heat equation with a noise term in this paper we study blow up of the equation u t u xx u gamma dot w tx where dot w tx is a two dimensional white noise field and where dirichlet boundary conditions are enforced it is known that if 3 2 then the solution exists for all time in this paper we show that if is much larger than 3 2 then the solution blows up in finite time with positive probability we prove this by considering how peaks in the solution propagate if a peak of high mass forms we rescale the equation and divide the mass of the peak into a collection of peaks of smaller mass and these peaks evolve almost independently in this way we compare the evolution ofu to a branching process large peaks are regarded as particles in this branching process offspring are peaks which are higher by some factor we show that the expected number of offspring is greater than one when is much larger than 3 2 and thus the branching process survives with positive probability corresponding to blowup in finite time