Invariant Measure of Approximating Method for Stochastic Functional Differential Equation

Abstract

This paper establishes the sufficient criteria for the stability in distribution of numerical solutions for the stochastic functional differential equation (SFDE) with infinite delay. We first check the mean-square boundedness and convergence of numerical solutions from different initial data and prove the existence of the invariant measure of the approximate segment process under suitable conditions. Then, we show that the numerical stationary distribution converges to the stationary distribution of the underlying solution.

Keywords

Stationary distribution / Infinite delay / Stochastic functional differential equation (SFDE) / 34F05 / 34E10 / 37L55 / 70K65

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Funding

Innovative Research Group Project of the National Natural Science Foundation of China(12471279)

Rights & permissions

Shanghai University