Stationary distribution of the stochastic theta method for nonlinear stochastic differential equations

TL;DR

This paper investigates the stationary distribution properties of the stochastic theta method for nonlinear stochastic differential equations, analyzing how parameter choices affect convergence and demonstrating results through numerical experiments.

Contribution

It provides a theoretical analysis of the stationary distribution existence, uniqueness, and convergence for the stochastic theta method under various parameter settings.

Findings

Stationary distribution exists and is unique under certain conditions.

Convergence of numerical to true stationary distribution is established.

Numerical experiments confirm theoretical predictions.

Abstract

The existence and uniqueness of the stationary distribution of the numerical solution generated by the stochastic theta method is studied. When the parameter theta takes different values, the requirements on the drift and diffusion coefficients are different. The convergence of the numerical stationary distribution to the true counterpart is investigated. Several numerical experiments are presented to demonstrate the theoretical results.