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

2009/09/18 by Coulibaly-Pasquier, Koléhé Abdoulaye
#(53C44 #58J65 #60G46 #60J65) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0909.3359

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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