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Averaging of semigroups associated to diffusion processes on a simplex

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  • Faure, Dimitri

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.

Suggested Citation

  • Faure, Dimitri, 2022. "Averaging of semigroups associated to diffusion processes on a simplex," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 323-357.
    • Handle: RePEc:eee:spapps:v:150:y:2022:i:c:p:323-357
    DOI: 10.1016/j.spa.2022.04.014
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    References listed on IDEAS

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    1. Titulaer, U.M., 1978. "A systematic solution procedure for the Fokker-Planck equation of a Brownian particle in the high-friction case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 91(3), pages 321-344.
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