Numerical Scheme for the Invariant Measure of Highly Nonlinear McKean–Vlasov Stochastic Differential Equation
Abstract
To approximate the invariant measure of McKean–Vlasov stochastic differential equation (MVSDE) with highly nonlinear drift and diffusion coefficients, this paper constructs the backward Euler scheme for the corresponding self-interacting stochastic differential equation (SDE), which depends on both current and historical information. Then the empirical measure of the numerical solution for self-interacting SDE is proved to converge to the invariant measure of the original MVSDE under the Wasserstein distance. The numerical simulations are provided to support this finding.
Fields of Study & Subjects
Stochastic processes and financial applications
Numerical methods for differential equations
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- Fluctuation and Noise Letters
- Volume
- 25
- Issue
- 03
- Publication date
- 11 February 2026
- Language
- EN