[PDF] Top 20 Backward stochastic evolution equations in infinite dimensions

... Such equations have proved to be very useful in the study of the adjoint equation of an optimal control of a quasilinear stochastic heat equation, see [37], in which the Wiener filtratio[r] ... See full document

... This article presents the results on existence, uniqueness and sta- bility of mild solutions to neutral stochastic functional evolu- tion integro-differential equations with non-Lipschitz condition and ... See full document

... differential equations. Al- most periodic solutions of stochastic differential equations driven by white Gaussian noise have been studied extensively for the reason that random fluctuations come ... See full document

... of stochastic differential equa- tions (SDE) on a Hilbert space with cylindrical Wiener noise, whose non- linear drift parts are sums of the sub-differential of a convex function and a bounded ...finite ... See full document

... In [2], Lions has discussed the existence and uniqueness of solutions for system (1.5) and gave an existence and uniqueness result. In [1], Hu and Peng considered the existence and uniqueness of solutions for a class of ... See full document

... In this paper, we study fully coupled FBSDEs driven by a martingale generated by a continuous-time finite-state Markov chain. Inspired by Peng and Wu [], we introduce an m × n full-rank matrix G to overcome the problem ... See full document

... so-called ‘evolutionary equations’, see [6]. With this notion, it is possible to obtain a distributional solution of ( ∗ ) such that the differential algebraic equa- tion holds in an integrated sense, where the ... See full document

... to stochastic differential equations with Markovian ...of stochastic differential equations has always lain at the center of our understanding concerning stochastic models de- scribed ... See full document

... field equations involves two limit ...to infinite dimensional state space is ob- tained by a continuum ...integro-differential equations such as the Wilson–Cowan equation ...jump evolution ... See full document

... o stochastic differential ...an infinite dimensional approach based on semigroup theory has been used, providing a deterministic Kolmogorov equation associated to a SDDE driven by a Brownian ...of ... See full document

... differential equations is emerging as an active area of investigation due to the application in area such as mechanics, electrical engineering, medicine biology, and ecology, see Benchohra and Henderson [3], Hern´ ... See full document

... second-order stochastic differential equa- tions are the right model in continuous time to account for integrated processes that can be made ...second-order stochastic differential ...second-order ... See full document

... finite dimensions of [18], [11], [7] and [16] show that by considering a general filtration ...more equations than those focused on just the Wiener filtration as for instance in [1], [4] or ... See full document

... In this paper, the solvability of a new kind of BSDE with the generator involving a finite- state Markov chain is studied. To overcome the difficulty applying the conventional ap- proach with the contraction mapping, an ... See full document

... The Cauchy problem of (super-parabolic) BSPDEs with quadratic growth in the second unknown variable arises naturally in the solution of the risk-sensitive optimal control problem as the associated Hamilton − Jacobi − ... See full document

... fractional stochastic impulsive neutral functional differential equations with infinite delay which arise from many practical applications such as viscoelasticity and ...the stochastic analysis ... See full document

... of stochastic partial differential equations by virtue of mean-field BDSDEs, which can be viewed as the stochastic Feynman-Kac formula for SPDEs of mean-field ... See full document

... the stochastic filtering formula, we derived the fil- tering equation and proved the existence and uniqueness of the filtering equation and the corresponding Nash equilibrium ... See full document

... fractional equations with infi- nite delay which possess the Lipschitz ...fractional evolution equations with Lipschitz condition was obtained by means of the monotone iter- ative technique by Mu in ... See full document

... The infinite sets of polynomial conserved densities which have been found for the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the Sine-Gordon equation, and the c[r] ... See full document