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.
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