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Stochastic Infinity-Laplacian equation and One-Laplacian equation in image processing and mean curvature flows : finite and large time behaviours

The existence of pathwise stationary solutions of this stochastic partial differential equation (SPDE, for abbreviation) is demonstrated. In Part II, a connection between certain kind of state constrained controlled Forward-Backward Stochastic Differential Equations (FBSDEs) and Hamilton-Jacobi-Bellman equations (HJB equations) are demonstrated. The special case provides a probabilistic representation of some geometric flows, including the mean curvature flows. Part II includes also a probabilistic proof of the finite time existence of the mean curvature flows.

Identiferoai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:554079
Date January 2010
CreatorsWei, Fajin
PublisherLoughborough University
Source SetsEthos UK
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Sourcehttps://dspace.lboro.ac.uk/2134/7345

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