We propose a general framework to implement an Euler like approximation method for stochastic equations under the Wasserstein distance. The framework originates from explicit results for the diffusion case due to Lamberton and Pages, Pages and Panloup between others. We believe that the proposed general framework applies to many examples. In particular, we show that it applies to Langevin type equations, reflected equations, Boltzmann type stochastic equations and some neuronal models. This framework is built using some basic ideas from the sewing lemma.
This is ongoing joint work with V. Bally (U. G. Eiffel) and A. Alfonsi (ENPC).
A general framework for an approximation method for invariant measures of stochastic equations
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