robust decoding for convolutionally coded systems impaired by memoryless impulsive noise it is well known that communication systems are susceptible to strong impulsive noises to combat this convolutional coding has long served as a cost efficient tool against moderately frequent memoryless impulses with given statistics nevertheless impulsive noise statistics are difficult to model accurately and are typically not time invariant making the system design challenging in this paper because of the lack of knowledge regarding the probability density function of impulsive noises an efficient decoding scheme was devised for single carrier narrowband communication systems a design parameter was incorporated into recently introduced joint erasure marking and viterbi decoding algorithm dubbed the metric erasure viterbi algorithm meva the proposed scheme involves incorporating a well designed clipping operation into a viterbi algorithm in which the clipping threshold must be appropriately set in contrast to previous publications that have resorted to extensive simulations in the proposed scheme the bit error probability performance associated with the clipping threshold was characterized by deriving its chernoff bound the results indicated that when the clipping threshold was judiciously selected the meva can be on par with its optimal maximum likelihood decoding counterpart under fairly general circumstances

weak dynamic programming principle for viscosity solutions we prove a weak version of the dynamic programming principle for standard stochastic control problems and mixed control stopping problems which avoids the technical difficulties related to the measurable selection argument in the markov case our result is tailor made for the derivation of the dynamic programming equation in the sense of viscosity solutions

saddlepoint approximations for continuous time markov processes this paper proposes saddlepoint expansions as a means to generate closed form approximations to the transition densities and cumulative distribution functions of markov processes this method is applicable to a large class of models considered in finance for which a laplace or characteristic functions but not the transition density can be found in closed form but even when such a computation is not possible explicitly we go one step further by showing how useful approximations can be obtained by replacing the laplace or characteristic functions by an expansion in small time

curvature characteristics and congruence of the thumb carpometacarpal joint differences between female and male joints abstract three dimensional geometric models of the articular surfaces of the thumb carpometacarpal cmc joint were constructed using precise data obtained from stereophotogrammetry spg it was demonstrated that by using a least squares surface fitting technique the spg data on the surface can accurately be described by a single parametric biquintic spline function from this mathematical description curvature maps of the surfaces were calculated for 13 cmc joints eight females average 64 yr old five males average 70 yr old the surface geometry of each joint was analyzed comparisons were made between trapezial and metacarpal surfaces of the joint and differences determined between males and females with regard to joint surface areas the female trapezium is significantly smaller than that of the metacarpal the shape of the female trapezial surface is also fundamentally different from of males no gender related difference exists regarding the shape of the metacarpal surface congruence of the two opposing articular surfaces was defined by their relative principal curvatures from these definitions congruence in the radioulnar and dorsovolar anatomic directions as well as the global congruence of the joint were calculated most cmc joints were found to be more congruent along the radioulnar direction than the dorsovolar direction and globally female joints were found to be less congruent than male joints the concept of joint congruence has played a central role in a number of hypotheses relating to the etiology of cmc joint osteoarthritis oa although conflicting hypotheses do exist the precise quantitative findings of this study may lead to an improved understanding of cmc joint oa and perhaps explain its prevalence in the female population over 55

convolutionally coded transmission over markov gaussian channels analysis and decoding metrics it has been widely acknowledged that the aggregate interference at the receiver for various practical communication channels can often deviate markedly from the classical additive white gaussian noise awgn assumption due to various ambient phenomena moreover the physical nature of the underlying interference generating process in such cases can lead to a bursty behaviour of the interfering signal implying that it is highly likely that consecutive symbols are affected by similar noise levels in this paper we devise and analyze detection techniques in conjunction with a convolution code for such interference channels that possess non negligible memory by considering optimum and sub optimum decoding metrics in particular the inherent memory in the noise process is modeled as a first order markov chain whose state selects the variance of the instantaneous gaussian noise leading to a markov gaussian channel model analytical expressions are obtained for the cut off rate which is an ensemble code parameter and the bit error rate for a convolutionally coded system that are subsequently employed for an extensive evaluation of the various metrics considered furthermore the interleaving depth is considered as a design parameter and its effect on performance is analyzed over a range of noise scenarios

two person zero sum game in weak formulation and path dependent bellman isaacs equation in this paper we study a two person zero sum stochastic differential game in weak formulation unlike the standard literature which uses strategy type controls the weak formulation allows us to consider the game with control against control we shall prove the existence of game value under natural conditions another main feature of the paper is that we allow for non markovian structure and thus the game value is a random process we characterize the value process as the unique viscosity solution of the corresponding path dependent bellman isaacs equation a notion recently introduced by ekren et al ann probab 42 2014 pp 204 236 and ekren touzi and zhang stochastic process to appear preprint arxiv 1210 0006v2 preprint arxiv 1210 0007v2

superhedging and dynamic risk measures under volatility uncertainty we consider dynamic sublinear expectations i e time consistent coherent risk mea sures whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty we derive a cadlag nonlinear martingale which is also the value process of a superhedg ing problem the superhedging strategy is obtained from a representation similar to the optional decomposition furthermore we prove an optional sampling theorem for the nonlinear martingale and characterize it as the solution of a second order backward sde the uniqueness of dynamic extensions of static sublinear expectations is also studied

performance analysis for bicm transmission over gaussian mixture noise fading channels bit interleaved coded modulation bicm has been adopted in many systems and standards for spectrally efficient coded transmission the analytical evaluation of bicm performance parameters in particular bit error rate ber has received considerable attention in the recent past in this paper we derive ber approximations for bicm transmission over general fading channels impaired by gaussian mixture noise gmn to this end we build upon the saddlepoint approximation of the pairwise error probability pep and a recently established approximation for the probability density function pdf of bit wise reliability metrics for nonfading additive white gaussian noise awgn channels we extend this pdf approximation to the case of gmn and obtain closed form expressions for its laplace transform for fading gmn channels the latter allows us to express the pep and thus ber via the saddlepoint approximation for the special case of fading awgn channels the presented approximations are closed form since the saddlepoint is well approximated by 1 2 for bicm decoding furthermore we derive closed form pep expressions also for gmn channels in the high signal to noise ratio regime and establish the diversity and coding gain for bicm transmission over fading gmn channels selected numerical results for the ber of convolutional coded bicm highlight the usefulness of the proposed approximations and the differences between awgn and gmn channels

on viscosity solutions of path dependent pdes in this paper we propose a notion of viscosity solutions for path dependent semi linear parabolic pdes this can also be viewed as viscosity solutions of non markovian backward sdes and thus extends the well known nonlinear feynman kac formula to non markovian case we shall prove the existence uniqueness stability and comparison principle for the viscosity solutions the key ingredient of our approach is a functional ito calculus recently introduced by dupire functional ito calculus 2009 preprint

approximation of achievable rates in additive gaussian mixture noise channels in this paper we detail effective methods to approximate the achievable rates of channels with additive gaussian mixture gm noise for both real and complex channels to achieve any desired level of accuracy attention is paid to a gaussian input a discrete real input and a complex input with discrete amplitude and independent uniform phase such discrete inputs represent a wide range of input distributions and they include the capacity achieving inputs as special cases at first we propose a simple technique to accurately calculate the noise entropy specifically when the noise level is high a lower bound on the integrand of the entropy is established and the noise entropy can be estimated using a closed form solution in the low noise region the piecewise linear curve fitting pwlcf method is applied we then extend this result to calculate the achievable rate when the input is gaussian distributed which is shown to be asymptotically optimal next we propose a simple pwlcf based method to approximate the output entropy for a real gm channel when the input is discrete and for a complex gm channel when the input is discrete in amplitude with independent uniform phase in particular for the real channel the output entropy is evaluated by examining the output in high and low regions of amplitude using a lower bound on the integrand of the output entropy and pwlcf respectively for the complex channel the output entropy is approximated a similar manner but using polar coordinates and the kernel function it is demonstrated that the output entropy and consequently the achievable rates can be computed to achieve any given accuracy level

signed rank nonparametric multiuser detection in non gaussian channels we present a novel nonparametric multiuser detector for non gaussian channels that is based on the signed rank norm for linear regression analytical and simulation results show that the proposed detector offers similar or better performance as compared to the minimax robust detector but without requiring any a priori information on the noise the complexity of this detector is lower than that of the pseudo norm nonparametric detector stated previously by the authors this is due to the fact that in contrast to the latter it is not necessary to compute the intercept parameter for the signed rank detector proposed in this correspondence we analyze the behavior of the blind version of this detector and show that it outperforms the blind minimax detector we also show that this detector has a bounded influence function and hence it is robust

pricing early exercise and discrete barrier options by fourier cosine series expansions we present a pricing method based on fourier cosine expansions for early exercise and discretely monitored barrier options the method works well for exponential levy asset price models the error convergence is exponential for processes characterized by very smooth rm c infty a b in mathbb r transitional probability density functions the computational complexity is o m 1 n log n with n a small number of terms from the series expansion and m the number of early exercise monitoring dates this paper is the follow up of fang and oosterlee in siam j sci comput 31 2 826 848 2008 in which we presented the impressive performance of the fourier cosine series method for european options

the accuracy of joint surface models constructed from data obtained with an electromagnetic tracking device electromagnetic tracking devices are widely used in biomechanics in this article a method is evaluated to construct models of articular surfaces using an electromagnetic tracking device first the accuracy of the space tracker was examined and optimised then from several joint surfaces random points were measured and eighth degree polynomials were fitted to these measurements to check if the fit converged well plots of cross sections of the model with corresponding data points were examined the accuracy of the models was determined by comparing them with computed tomography data and by reproducibility tests all the fits converged well to the data the root mean square rms error of the models varied from 0 07 to 0 18mm and was proportional to the size and complexity of the surface this was mainly due to systematic errors made by the space tracker which were also proportional to the size and complexity of the surface

feynman kac representation for hamilton jacobi bellman ipde we aim to provide a feynman kac type representation for hamilton jacobi bellman equation in terms of forward backward stochastic differential equation fbsde with a simulatable forward process for this purpose we introduce a class of bsde where the jumps component of the solution is subject to a partial nonpositive constraint existence and approximation of a unique minimal solution is proved by a penalization method under mild assumptions we then show how minimal solution to this bsde class provides a new probabilistic representation for nonlinear integro partial differential equations ipdes of hamilton jacobi bellman hjb type when considering a regime switching forward sde in a markovian framework moreover we state a dual formula of this bsde minimal solution involving equivalent change of probability measures this gives in particular an original representation for value functions of stochastic control problems including controlled diffusion coefficient

parameter estimation for middleton class a interference processes the problem of estimating the parameters of the middleton class a interference model is considered on the assumption of the availability of a set of independent samples from class a envelope distribution the asymptotic performances of several estimation procedures are explored from this analysis estimates based on the method of moments are seen to be consistent and computationally desirable but highly inefficient whereas more efficient likelihood based estimators are seen to be computationally unwieldy however an estimator that initiates likelihood iteration with the method of moments estimates is seen to overcome these difficulties in its asymptotic performance unfortunately simulation of this third estimator for practical sample sizes reveals poor performance under these conditions to overcome this lack of small sample efficiency a similar estimator that initiates likelihood iteration with physically motivated but nonoptimal estimates is also proposed simulation of this latter estimator for practical sample sizes indicates that near optimal performance is attained by this technique

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

martingale optimal transport and robust hedging in continuous time the duality between the robust or equivalently model independent hedging of path dependent european options and a martingale optimal transport problem is proved the financial market is modeled through a risky asset whose price is only assumed to be a continuous function of time the hedging problem is to construct a minimal super hedging portfolio that consists of dynamically trading the underlying risky asset and a static position of vanilla options which can be exercised at the given fixed maturity the dual is a monge kantorovich type martingale transport problem of maximizing the expected value of the option over all martingale measures that have a given marginal at maturity in addition to duality a family of simple piecewise constant super replication portfolios that asymptotically achieve the minimal super replication cost is constructed

a new approach for surface fitting method of articular joint surfaces the application of joint contact mechanics requires a precise configuration of the joint surfaces b spline and nurbs have been widely used to model joint surfaces but because these formulations use a structured data set provided by a rectangular net first then a grid there is a limit to the accuracy of the models they can produce however new imaging systems such as 3d laser scanners can provide more realistic unstructured data sets what is needed is a method to manipulate the unstructured data we created a parametric polynomial function and applied it to unstructured data sets obtained by scanning joint surfaces we applied our polynomial model to unstructured data sets from an artificial joint and confirmed that our polynomial produced a smoother and more accurate model than the conventional b spline method next we applied it to a diarthrodial joint surface containing many ripples and found that our function s noise filtering characteristics smoothed out existing ripples since no formulation was found to be optimal for all applications we used two formulations to model surfaces with ripples first we used our polynomial to describe the global shape of the objective surface minute undulations were then specifically approximated with a fourier series function finally both approximated surfaces were superimposed to reproduce the original surface in a complete fashion

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

a statistical and physical mechanisms based interference and noise model for array observations a statistical noise model is developed from mathematical modeling of the physical mechanisms that generate noise in communication receivers employing antenna arrays such models have been lacking for cases where the antenna observations may be statistically dependent from antenna to antenna the model is developed by generalizing an approach for single antenna cases suggested by middleton 1967 1974 1976 1977 the model derived here is applicable to a wide variety of physical situations the focus is primarily on problems defined by middleton to be class a interference the number of noise sources in a small region of space is assumed to be poisson distributed and the emission times are assumed to be uniformly distributed over a long time interval finally an additive gaussian background component is included to represent the thermal noise that is always present in real receivers

recombined multinomial tree based on saddle point approximation and its application to levy models options pricing abstract this paper studies the constructing methods of a recombined multinomial tree based on saddle point approximation and its application to levy models options pricing firstly the levy process and the european option pricing are introduced then we used the characteristic function of levy process to generate density function value at discrete point in a certain range based on the saddle point approximation method then we provide the method to construct recombined multinomial tree and give the pricing formula of european option and path dependent option pricing based on the backward iteration finally we used the cgmy process to demonstrate its application to european option american option and american barrier option pricing it proves that saddle point approximation turns the inverse fourier integral transform problem to several function value calculation comparing to ifft the speed of calculation using this method is faster and it avoid the negative probability density function value based on ifft because of the linear growth of the number of nodes we can extend the saddle point approximation method to the calculation of path dependent option

sequence detection and adaptive channel estimation for isi channels under class a impulsive noise in this paper sequence detection and channel estimation for frequency selective intersymbol interference isi producing channels under class a impulsive noise are considered we introduce a novel suboptimum sequence detection ssd scheme and show that although ssd employs a simplified metric it achieves practically the same performance as maximum likelihood sequence detection mlsd for both ssd and mlsd a lower bound on the achievable performance is derived which is similar to the classical matched filter bound for frequency selective fading channels under gaussian noise for channel estimation we adopt a minimum entropy criterion and derive efficient least mean entropy and recursive least entropy algorithms for both adaptive algorithms we analyze the steady state channel estimation error variance theoretical considerations and simulation results show that in class a impulsive noise the proposed sequence detection and adaptive channel estimation schemes yield significant performance gains over their respective conventional counterparts designed for gaussian noise although the novel algorithms require knowledge of the class a noise model parameters their computational complexity is comparable to that of the corresponding conventional algorithms

signal detection in multivariate class a interference the aim of this article is to identify and evaluate multivariate density functions when the univariate densities are all class a three models are proposed model a for independent random variables model b for dependent random variables model c for uncorrelated random variables for each model the structure of the marginal densities moments and characteristic functions are evaluated truncated forms for the multivariate densities are proposed the error and percentage error due to truncation are evaluated numerically for the two dimensional case finally a signal detection problem is examined the performance of the optimal detector is compared to that achieved by the detector designed using truncated density functions it is shown that the performance difference is negligible when the model parameters are small

three dimensional mathematical model analysis of the patellofemoral joint this paper is concerned with a mathematical model analysis of the patellofemoral joint in the human knee taking into account the articular surface geometry and mechanical properties of the ligament it was made by the application of a computer aided design theory previously studied and it was possible to express the articular surface geometries in a mathematical formulation and hence elucidate the joint movement mechanics this method was then applied to a three dimensional geometrical model of the patellofemoral joint for the modelling of tendofemoral contact at large angles of knee flexion the geodestic line theory was adopted applying the newton raphson method and the runge kutta gil method to the model variables such as patellar attitudes patellofemoral contact force and tensile force of the patellar ligament for various knee flexion angles were computed applying the hertzian elastic theory contact stress was also computed these results showed good agreement with the previously reported experimental results as an application for the model some parameter analyses were performed in terms of the contact stress variations and compared with those of the normal knee the simulation results indicated that both the q angle increase and decrease increased contact stress the patella alta showed undulating variations of stress while the patella infera showed little change of stress and the tibial tuberositas elevation showed 20 30 reduction of stress

a highly efficient shannon wavelet inverse fourier technique for pricing european options in the search for robust accurate and highly efficient financial option valuation techniques we here present the swift method shannon wavelets inverse fourier technique based on shannon wavelets swift comes with control over approximation errors made by means of sharp quantitative error bounds the nature of the local shannon wavelets basis enables us to adaptively determine the proper size of the computational interval numerical experiments on european style options show exponential convergence and confirm the bounds robustness and efficiency

nonlinear levy processes and their characteristics we develop a general construction for nonlinear levy processes with given characteristics more precisely given a set of levy triplets we construct a sublinear expectation on skorohod space under which the canonical process has stationary independent increments and a nonlinear generator corresponding to the supremum of all generators of classical levy processes with triplets in the nonlinear levy process yields a tractable model for knightian uncertainty about the distribution of jumps for which expectations of markovian functionals can be calculated by means of a partial integro dierenti al equation

two dimensional fourier cosine series expansion method for pricing financial options the cos method for pricing european and bermudan options with one underlying asset was developed in f fang and c w oosterlee siam j sci comput 31 2008 pp 826 848 and f fang and c w oosterlee numer math 114 2009 pp 27 62 in this paper we extend the method to higher dimensions with a multidimensional asset price process the algorithm can be applied to for example pricing two color rainbow options but also to pricing under the popular heston stochastic volatility model for smooth density functions the resulting method converges exponentially in the number of terms in the fourier cosine series summations otherwise we achieve algebraic convergence the use of an fft algorithm for asset prices modeled by levy processes makes the algorithm highly efficient we perform extensive numerical experiments

fitting parametrized polynomials with scattered surface data currently used joint surface models require the measurements to be structured according to a grid with the currently available tracking devices a large quantity of unstructured surface points can be measured in a relatively short time in this paper a method is presented to fit polynomial functions to three dimensional unstructured data points to test the method spherical cylindrical parabolic hyperbolic exponential logarithmic and sellar surfaces with different undulations were used the resulting polynomials were compared with the original shapes the results show that even complex joint surfaces can be modelled with polynomial functions in addition the influence of noise and the number of data points was also analyzed from a surface diam 20 mm which is measured with a precision of 0 2 mm a model can be constructed with a precision of 0 02 mm

viscosity solutions of fully nonlinear parabolic path dependent pdes part ii the main objective of this paper and the accompanying one viscosity solutions of fully nonlinear parabolic path dependent pdes part ii 2012 preprint is to provide a notion of viscosity solutions for fully nonlinear parabolic path dependent pdes our definition extends our previous work ann probab 2014 42 204 236 focused on the semilinear case and is crucially based on the nonlinear optimal stopping problem analyzed in stochastic process appl 2014 124 3277 3311 we prove that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions and satisfies a stability property and a partial comparison result the latter is a key step for the well posedness results established in viscosity solutions of fully nonlinear parabolic path dependent pdes part ii 2012 preprint we also show that the value processes of path dependent stochastic control problems are viscosity solutions of the corresponding path dependent dynamic programming equations

stochastic target games and dynamic programming via regularized viscosity solutions we study a class of stochastic target games where one player tries to find a strategy such that the state process almost surely reaches a given target no matter which action is chosen by the opponent our main result is a geometric dynamic programming principle which allows us to characterize the value function as the viscosity solution of a non linear partial differential equation because abstract measurable selection arguments cannot be used in this context the main obstacle is the construction of measurable almost optimal strategies we propose a novel approach where smooth supersolutions are used to define almost optimal strategies of markovian type similarly as in verification arguments for classical solutions of hamilton jacobi bellman equations the smooth supersolutions are constructed by an extension of krylov s method of shaken coefficients we apply our results to a problem of option pricing under model uncertainty with different interest rates for borrowing and lending

bsdes driven by g brownian motion with time varying lipschitz condition abstract the present paper is devoted to the study of backward stochastic differential equations driven by g brownian motion g bsdes with time varying lipschitz condition with the help of nonlinear stochastic analysis technique and approximation method we prove that the g bsdes admit a unique solution on finite or infinite time horizon furthermore we obtain the corresponding comparison theorem

wellposedness of second order backward sdes we provide an existence and uniqueness theory for an extension of backward sdes to the second order while standard backward sdes are naturally connected to semilinear pdes our second order extension is connected to fully nonlinear pdes as suggested in cheridito et al commun pure appl math 60 7 1081 1110 2007 in particular we provide a fully nonlinear extension of the feynman kac formula unlike cheridito et al in commun pure appl math 60 7 1081 1110 2007 the alternative formulation of this paper insists that the equation must hold under a non dominated family of mutually singular probability measures the key argument is a stochastic representation suggested by the optimal control interpretation and analyzed in the accompanying paper soner et al in dual formulation of second order target problems arxiv 1003 6050 2009

the dynamic programming equation for second order stochastic target problems motivated by applications in mathematical finance u cetin h m soner and n touzi options hedging for small investors under liquidity costs finance stoch to appear we continue our study of second order backward stochastic equations in this paper we derive the dynamic programming equation for a certain class of problems which we call the second order stochastic target problems in contrast with previous formulations of similar problems we restrict control processes to be continuous this new framework enables us to apply our results to a larger class of models also the resulting derivation is more transparent the main technical tool is the geometric dynamic programming principle in this context and it is proved by using the framework developed in h m soner and n touzi j eur math soc jems 8 2002 pp 201 236

maximum principle for forward backward stochastic control system under g expectation and relation to dynamic programming in this paper based on the theory of stochastic differential equations on a sublinear expectation space h e we develop a stochastic maximum principle for a general forward backward stochastic control system under g expectation under some convexity assumptions we also obtain sufficient conditions for the optimality furthermore relations between the adjoint processes and the value function for stochastic recursive optimal control problems are given finally applications of our main results to the recursive utility portfolio optimization problem in financial market are discussed

constrained optimal transport the classical duality theory of kantorovich c r doklady acad sci urss ns 37 199 201 1942 and kellerer z wahrsch verw gebiete 67 4 399 432 1984 for classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided this abstract generalization is set in a banach lattice mathcal x with an order unit the problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of mathcal x and the dual problem is defined on the bi dual of mathcal x these results are then applied to several extensions of the classical optimal transport

stochastic control for a class of nonlinear kernels and applications we consider a stochastic control problem for a class of nonlinear kernels more precisely our problem of interest consists in the optimization over a set of possibly non dominated probability measures of solutions of backward stochastic differential equations bsdes since bsdes are non linear generalizations of the traditional linear expectations this problem can be understood as stochastic control of a family of nonlinear expectations or equivalently of nonlinear kernels our first main contribution is to prove a dynamic programming principle for this control problem in an abstract setting which we then use to provide a semimartingale characterization of the value function we next explore several applications of our results we first obtain a wellposedness result for second order bsdes as introduced in 76 which does not require any regularity assumption on the terminal condition and the generator then we prove a non linear optional decomposition in a robust setting extending recent results of 63 which we then use to obtain a superhedging duality in uncertain incomplete and non linear financial markets finally we relate under additional regularity assumptions the value function to a viscosity solution of an appropriate path dependent partial differential equation ppde

capacity achieving input distributions of additive quadrature gaussian mixture noise channels this paper studies the characterization of the optimal input and the computation of the capacity of additive quadrature gaussian mixture gm noise channels under an average power constraint the considered model can be used to represent a wide variety of channels with impulsive interference such as the well known bernoulli gaussian and middleton class a impulsive noise channels as well as multiple access interference channels and cognitive radio channels under imperfect sensing at first we demonstrate that there exists a unique input distribution that achieves the channel capacity and the capacity achieving input distribution has a uniformly distributed phase by examining the kuhn tucker alignment conditions ktcs we further show that if the optimal input amplitude distribution contains an infinite number of mass points on a bounded interval the channel output must be gaussian distributed however by using bernstein s theorem to examine the completely monotonic condition it is shown that the assumption of a gaussian distributed output is not valid as a result there are always a finite number of mass points on any bounded interval in the optimal amplitude distribution in addition by applying a novel bounding technique on the ktc and using the envelop theorem we demonstrate that the optimal amplitude distribution cannot have an infinite number of mass points this gives us the unique solution of the optimal input having discrete amplitude with a finite number of mass points given this discrete nature of the optimal input we then develop a simple method to compute the discrete optimal input and the corresponding capacity our numerical examples show that in many cases the capacity achieving distribution consists of only one or two mass points

performance bounds for optimum and suboptimum reception under class a impulsive noise the transmission over the memoryless additive white class a noise awcn channel is considered for uncoded transmission an exact expression for the symbol error rate is derived for coded transmission the chernoff bound on the pairwise error probability is calculated and the performance achieved on the real and the complex awcn channels is compared moreover a low complexity suboptimum decoding metric is derived and analyzed employing the cutoff rate as a performance criterion

comparison of viscosity solutions of semi linear path dependent pdes this paper provides a probabilistic proof of the comparison result for viscosity solutions of path dependent semilinear pdes we consider the notion of viscosity solutions introduced in 8 which considers as test functions all those smooth processes which are tangent in mean when restricted to the markovian case this definition induces a larger set of test functions and reduces to the notion of stochastic viscosity solutions analyzed in 1 2 our main result takes advantage of this enlargement of the test functions and provides an easier proof of comparison this is most remarkable in the context of the linear path dependent heat equation as a key ingredient for our methodology we introduce a notion of punctual differentiation similar to the corresponding concept in the standard viscosity solutions 3 and we prove that semimartingales are almost everywhere punctually differentiable this smoothness result can be viewed as the counterpart of the aleksandroff smoothness result for convex functions a similar comparison result was established earlier in 8 the result of this paper is more general and more importantly the arguments that we develop do not rely on any representation of the solution

perpetual american options under levy processes we consider perpetual american options assuming that under a chosen equivalent martingale measure the stock returns follow a levy process for put and call options their analogues for more general payoffs and a wide class of levy processes that contains brownian motion normal inverse gaussian processes hyperbolic processes truncated levy processes and their mixtures we obtain formulas for the optimal exercise price and the fair price of the option in terms of the factors in the wiener hopf factorization formula i e in terms of the resolvents of the supremum and infimum processes and derive explicit formulas for these factors for calls puts and some other options the results are valid for any levy process we use dynkin s formula and the wiener hopf factorization to find the explicit formula for the price of the option for any candidate for the exercise boundary and by using this explicit representation we select the optimal solution we show that in some cases the principle of the smooth fit fails and suggest a generalization of this principle

probabilistic interpretation for solutions of fully nonlinear stochastic pdes in this article we propose a wellposedness theory for a class of second order backward doubly stochastic differential equation 2bdsde we prove existence and uniqueness of the solution under a lipschitz type assumption on the generator and we investigate the links between the 2bdsdes and a class of parabolic fully nonlinear stochastic pdes precisely we show that the markovian solution of 2bdsdes provide a probabilistic interpretation of the classical and stochastic viscosity solution of fully nonlinear spdes

second order backward stochastic differential equations and fully nonlinear parabolic pdes for a d dimensional diffusion of the form dxt xt dt xt dwt and continuous functions f and g we study the existence and uniqueness of adapted processes y z and a solving the second order backward stochastic differential equation 2bsde dyt f t xt yt zt t dt z dxt t 0 t dzt at dt t dxt

bsdes with weak terminal condition we introduce a new class of backward stochastic differential equations in which the t terminal value y t of the solution y z is not fixed as a random variable but only satisfies a weak constraint of the form e psi y t ge m for some possibly random non decreasing map psi and some threshold m we name them textit bsdes with weak terminal condition and obtain a representation of the minimal time t values y t such that y z is a supersolution of the bsde with weak terminal condition it provides a non markovian bsde formulation of the pde characterization obtained for markovian stochastic target problems under controlled loss in bouchard elie and touzi we then study the main properties of this minimal value in particular we analyze its continuity and convexity with respect to the m parameter appearing in the weak terminal condition and show how it can be related to a dual optimal control problem in meyer form these last properties generalize to a non markovian framework previous results on quantile hedging and hedging under loss constraints obtained in follmer and leukert and in bouchard elie and touzi finally we observe a surprisingly strong connection between bsdes with weak terminal condition and 2nd order bsdes in the quasi linear case

iterative decoding of codes over complex numbers for impulsive noise channels we discuss the decoding of error correcting block codes over complex numbers for the transmission over impulsive noise channels the encoder multiplies a vector of complex information symbols resulting from a modulation scheme e g quadrature amplitude modulation qam with a unitary generator matrix g choosing the inverse fourier transform as g the encoding procedure is similar to orthogonal frequency division multiplex ofdm modulation the maximum a posteriori map receiver is analyzed and a suboptimum decoder based on the turbo decoding principle is derived simulation results show the excellent performance of the iterative decoder