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

Koléhé Abdoulaye Coulibaly-Pasquier (1)

1 IECN - Institut Élie Cartan de Nancy

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.

Mots clés: cicular brownian motion; mean curvature flow; stochastique process; differential equation

Domaines: Probabilités [math.PR]

Koléhé Abdoulaye Coulibaly-Pasquier. Some stochastic process without birth, linked to the mean curvature flow.. Annals of Probability, 2011, 39 (4), pp.1305--1331. ⟨10.1214/10-AOP580⟩. ⟨hal-00418303⟩