On the rate of convergence of finite-difference approximations for elliptic Isaacs equations in smooth domains

TL;DR

This paper establishes an algebraic rate of convergence for finite-difference solutions approximating uniformly elliptic Isaacs equations in smooth bounded domains, advancing numerical analysis in stochastic control.

Contribution

It proves the existence of an algebraic convergence rate for finite-difference schemes solving elliptic Isaacs equations in smooth domains, which was previously unknown.

Findings

Finite-difference solutions converge at an algebraic rate.

Convergence rate is established for smooth bounded domains.

Results improve understanding of numerical approximation for Isaacs equations.

Abstract

We show that the there exists an algebraic rate of convergence of solutions of finite-difference approximations for uniformly elliptic Isaacs in smooth bounded domains.