Solving Backward Doubly Stochastic Differential Equations through Splitting Schemes

TL;DR

This paper introduces a splitting scheme for backward doubly stochastic differential equations, decomposing them into simpler equations and approximating with finite difference schemes to achieve a first order numerical method.

Contribution

The paper presents a novel splitting scheme that simplifies solving backward doubly stochastic differential equations by decomposing and approximating with finite difference methods.

Findings

The proposed scheme converges at a first order rate.

Numerical experiments confirm the convergence rate.

The method effectively simplifies complex stochastic equations.

Abstract

A splitting scheme for backward doubly stochastic differential equations is proposed. The main idea is to decompose a backward doubly stochastic differential equation into a backward stochastic differential equation and a stochastic differential equation. The backward stochastic differential equation and the stochastic differential equation are then approximated by first order finite difference schemes, which results in a first order scheme for the backward doubly stochastic differential equation. Numerical experiments are conducted to illustrate the convergence rate of the proposed scheme.