Some stochastic process without birth, linked to the mean curvature flow
Probability
2009-09-21 v1
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 \'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.
Cite
@article{arxiv.0909.3359,
title = {Some stochastic process without birth, linked to the mean curvature flow},
author = {Koléhé Abdoulaye Coulibaly-Pasquier},
journal= {arXiv preprint arXiv:0909.3359},
year = {2009}
}