Some stochastic process without birth, linked to the mean curvature flow

Koléhé Abdoulaye Coulibaly-Pasquier

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arXiv · 0909.3359

Some stochastic process without birth, linked to the mean curvature flow

Koléhé Abdoulaye Coulibaly-Pasquier

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Abstract

Using Huisken results about the mean curvature flow on a strictly convex hypersurface, and Kendall-Cranston coupling, we will build a stochastic process without birth, and show that there exists a unique law of such process. This process has many similarities with the circular Brownian motions studied by Émery, Schachermayer, and Arnaudon. In general, this process is not a stationary process, it is linked with some differential equation without initial condition. We will show that this differential equation has a unique solution up to a multiplicative constant.

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Koléhé Abdoulaye Coulibaly-Pasquier. 2009-09-18. Some stochastic process without birth, linked to the mean curvature flow. https://arxiv.org/abs/0909.3359

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