In this paper, we consider the Cauchy problem of semi-linear degenerate backward stochastic partial differential equations (BSPDEs) under general settings without technical assumptions on the coefficients. For the solution of semi-linear degenerate BSPDE, we first give a proof for its existence...

In this paper we study the existence and uniqueness of the Lρ2p(Rd;R1)×Lρ2(Rd;Rd) valued solutions of backward doubly stochastic differential equations (BDSDEs) with polynomial growth coefficients using weak convergence, equivalence of norm principle and Wiener–Sobolev compactness arguments....

In this work we provide a stochastic representation for a class of semi-linear stochastic fractal equations, and prove the existence and uniqueness of Wρ1,p-solutions to stochastic fractal equations by using purely probabilistic argument, where ρ is a suitable weighted function, and Wρ1,p is...