On the discretization of backward doubly stochastic differential equations

TL;DR

This paper develops a discretization scheme for backward doubly stochastic differential equations by analyzing the regularity of the solution and applying Euler and Zhang methods for approximation.

Contribution

It introduces a novel discretization approach for (Y,Z) processes in backward doubly stochastic differential equations, combining Euler and Zhang schemes.

Findings

Proves L2-regularity of Z process.

Establishes convergence of the discretization scheme.

Provides error bounds for the approximation.

Abstract

In this paper, we are dealing with the approximation of the process (Y,Z) solution to the backward doubly stochastic differential equation with the forward process X . After proving the L2-regularity of Z, we use the Euler scheme to discretize X and the Zhang approach in order to give a discretization scheme of the process (Y,Z).