Euler-type approximation for the invariant measure: An abstract framework

Aurélien Alfonsi; Vlad Bally; Arturo Kohatsu-Higa

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arXiv · 2509.03971

Euler-type approximation for the invariant measure: An abstract framework

Aurélien Alfonsi·Vlad Bally·Arturo Kohatsu-Higa

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Abstract

We establish a general framework to study the rate of convergence of a Euler type approximation scheme with decreasing time steps to the invariant measure, for a general class of stochastic systems. The error is measured in general Wasserstein distances, which enables to encompass cases with non global contractivity conditions. Our main assumption is a coupling property which is expressed in terms of the one-step approximation. We show that the proposed set-up can be applied to a wide range of equations that may be law dependent, such as Langevin equations, reflected equations, Boltzmann type equations and for a recent McKean Vlasov type model for neuronal activity.

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Aurélien Alfonsi, Vlad Bally, Arturo Kohatsu-Higa. 2025-09-04. Euler-type approximation for the invariant measure: An abstract framework. https://arxiv.org/abs/2509.03971

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