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Title: Stochastic Infinity-Laplacian equation and One-Laplacian equation in image processing and mean curvature flows: finite and large time behaviours
Authors: Wei, Fajin
Keywords: Solutions
Stochastic partial differential equations
Random dynamical systems
Pathwise stationary
Viscosity solutions
Backward stochastic differential equations
Hamilton-Jacobi-Bellman equations
Mean curvature flows
Issue Date: 2010
Publisher: © Fajin Wei
Abstract: 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.
Description: A Doctoral Thesis. Submitted in partial fulfillment of the requirements for the award of Doctor of Philosophy of Loughborough University.
URI: https://dspace.lboro.ac.uk/2134/7345
Appears in Collections:PhD Theses (Maths)

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