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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
Infinity-Laplacian
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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