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

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

2009-09-18

arxiv.org/abs/0909.3359v1

Mathematics

Probability

Scientific paper

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 \'Emery, 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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