Numerical Computations for Backward Doubly SDEs and SPDEs

TL;DR

This paper introduces two numerical schemes for approximating solutions of backward doubly stochastic differential equations (BDSDEs), providing discretization methods, convergence proofs, and sample computations to demonstrate their effectiveness.

Contribution

The paper presents novel numerical discretization schemes for BDSDEs along with rigorous convergence proofs and practical computational examples.

Findings

Two effective numerical schemes for BDSDEs

Proofs of convergence for the proposed methods

Sample computations demonstrating applicability

Abstract

In this paper we present two numerical schemes of approximating solutions of backward doubly stochastic differential equations (BDSDEs for short). We give a method to discretize a BDSDE. And we also give the proof of the convergence of these two kinds of solutions for BDSDEs respectively. We give a sample of computation of BDSDEs.