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2019 Billiards with Markovian reflection laws
Clayton Barnes, Krzysztof Burdzy, Carl-Erik Gauthier
Electron. J. Probab. 24: 1-32 (2019). DOI: 10.1214/19-EJP398

Abstract

We use jump processes with stochastic intensity to construct a class of reflection laws for billiard processes in the unit interval whose stationary distribution for the billiard position and its velocity is the product of the uniform distribution and the standard normal distribution. These billiard processes have Markovian reflection laws, meaning their velocity is constant between reflections but changes in a Markovian way at reflection times.

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Clayton Barnes. Krzysztof Burdzy. Carl-Erik Gauthier. "Billiards with Markovian reflection laws." Electron. J. Probab. 24 1 - 32, 2019. https://doi.org/10.1214/19-EJP398

Information

Received: 9 February 2019; Accepted: 27 November 2019; Published: 2019
First available in Project Euclid: 31 December 2019

zbMATH: 07149387
MathSciNet: MR4049083
Digital Object Identifier: 10.1214/19-EJP398

Subjects:
Primary: 60J99
Secondary: 60K35

JOURNAL ARTICLE
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Vol.24 • 2019
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