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July 2011 Some stochastic process without birth, linked to the mean curvature flow
Koléhè A. Coulibaly-Pasquier
Ann. Probab. 39(4): 1305-1331 (July 2011). DOI: 10.1214/10-AOP580


Using Huisken’s results about the mean curvature flow on a strictly convex hypersurface and Kendall–Cranston’s coupling, we will build a stochastic process without birth and show that there exists a unique law of such a process. This process has many similarities with the circular Brownian motion studied by Émery and Schachermayer, and Arnaudon. In general this process is not a stationary process; it is linked to 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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Koléhè A. Coulibaly-Pasquier. "Some stochastic process without birth, linked to the mean curvature flow." Ann. Probab. 39 (4) 1305 - 1331, July 2011.


Published: July 2011
First available in Project Euclid: 5 August 2011

zbMATH: 1256.58013
MathSciNet: MR2857241
Digital Object Identifier: 10.1214/10-AOP580

Primary: 53C44 , 58J65 , 60B12 , 60G46 , 60J65

Keywords: Brownian motion , limit of stochastic processes , Mean curvature flow

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 4 • July 2011
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