Averaging of semigroups associated to diffusion processes on a simplex

Dimitri Faure

Stochastic Processes and their Applications, 2022, vol. 150, issue C, 323-357

Abstract: We study the averaging of a diffusion process living in a simplex K of Rn, n≥1. We assume that its infinitesimal generator can be decomposed as a sum of two generators corresponding to two distinct timescales and that the one corresponding to the fastest timescale is pure noise with a diffusion coefficient vanishing exactly on the vertices of K. We show that this diffusion process averages to a pure jump Markov process living on the vertices of K for the Meyer–Zheng topology. The role of the geometric assumptions done on K is also discussed.

Keywords: Diffusion processes; Homogenization theory; Averaging principle; Ergodic theorem; Meyer–Zheng topology; Jump Markov processes (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.04.014

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