L^{p}-solutions of backward doubly stochastic differential equations

TL;DR

This paper develops new stochastic calculus techniques to establish existence and uniqueness of L^{p}-solutions for backward doubly stochastic differential equations under weak data assumptions.

Contribution

It introduces novel technical methods and extends the existence and uniqueness results for BDSDEs to the L^{p} setting with p in (1,2).

Findings

Established a priori estimates for BDSDEs.

Proved existence and uniqueness of solutions in L^{p} for p in (1,2).

Extended previous results by Pardoux and Peng.

Abstract

The goal of this paper is to solve backward doubly stochastic differential equation (BDSDE, in short) under weak assumptions on the data. The first part is devoted to the development of some new technical aspects of stochastic calculus related to BDSDEs. Then we derive a priori estimates and prove existence and uniqueness of solutions in Lp, p\in (1,2), extending the work of pardoux and Peng (see Probab. Theory Related Fields 98 (1994), no. 2).