Homeomorphism of solutions to backward doubly SDEs and applications

TL;DR

This paper investigates the homeomorphic properties of solutions to one-dimensional backward doubly stochastic differential equations with parameter-dependent terminal values and applies these findings to certain second-order quasilinear parabolic stochastic PDEs.

Contribution

It establishes the homeomorphic properties of solutions to backward doubly SDEs and extends these results to specific classes of stochastic partial differential equations.

Findings

Solutions exhibit homeomorphic properties under certain conditions

Application to second order quasilinear parabolic stochastic PDEs demonstrated

Provides a framework for analyzing parameter-dependent stochastic differential equations

Abstract

In this paper we study the homeomorphic properties of the solutions to one dimensional backward doubly stochastic differential equations under suitable assumptions, where the terminal values depend on a real parameter. Then, we apply them to the solutions for a class of second order quasilinear parabolic stochastic partial differential equations.