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Pré-Publication, Document De Travail Année : 2018

Explicit speed of convergence of the stochastic billiard in a convex set

Résumé

In this paper, we are interested in the speed of convergence of the stochastic billiard evolving in a convex set K. This process can be described as follows: a particle moves at unit speed inside the set K until it hits the boundary, and is randomly reflected, independently of its position and previous velocity. We focus on convex sets in R 2 with a curvature bounded from above and below. We give an explicit coupling for both the continuous-time process and the embedded Markov chain of hitting points on the boundary, which leads to an explicit speed of convergence to equilibrium.
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Dates et versions

hal-01936931 , version 1 (27-11-2018)

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Ninon Fétique. Explicit speed of convergence of the stochastic billiard in a convex set. 2018. ⟨hal-01936931⟩
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