Discretization, Uniform-in-Time Estimations and Approximation of Invariant Measures for Nonlinear Stochastic Differential Equations with Non-Uniform Dissipativity

Shan Huang; Xiaoyue Li

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arXiv · 2511.12124

Discretization, Uniform-in-Time Estimations and Approximation of Invariant Measures for Nonlinear Stochastic Differential Equations with Non-Uniform Dissipativity

Shan Huang·Xiaoyue Li

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Abstract

The approximation of invariant measures for nonlinear ergodic stochastic differential equations (SDEs) is a central problem in scientific computing, with important applications in stochastic sampling, physics, and ecology. We first propose an easily applicable explicit Truncated Euler-Maruyama (TEM) scheme and prove its numerical ergodicity in the $L^p$-Wasserstein distance ($p\geqslant 1$). Furthermore, by combining truncation techniques with the coupling method, we establish a uniform-in-time $1/2$-order convergence rate in moments for the TEM scheme. Additionally, leveraging the exponential ergodicity of both the numerical and exact solutions, we derive a $1/2$-order convergence rate for the invariant measures of the TEM scheme and the exact solution in the $L^1$-Wasserstein distance. Finally, two numerical experiments are conducted to validate our theoretical results.

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Shan Huang, Xiaoyue Li. 2026-06-11. Discretization, Uniform-in-Time Estimations and Approximation of Invariant Measures for Nonlinear Stochastic Differential Equations with Non-Uniform Dissipativity. https://arxiv.org/abs/2511.12124

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