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Title (deu)
Numerical approximation of the stochastic total variation flow
Speaker / Lecturer
Martin Ondreját
Czech Academy of Sciences, Prague
Description (deu)
The talk is based on a joint work with L. Baňas (Bielefeld). We propose fully practical numerical schemes (conformal and non-conformal) for the simulation of the stochastic total variation flow (STVF). The approximation is based on a stable time-implicit finite element space-time approximation of a regularized STVF equation. The approximation also involves a finite dimensional discretization of the noise that makes the scheme fully implementable on physical hardware. We show that the proposed numerical scheme converges in law to a solution that is defined in the sense of stochastic variational inequalities (SVIs). Under strengthened assumptions the convergence can be show to holds even in probability. As a by product of our convergence analysis we provide a generalization of the concept of probabilistically weak solutions of stochastic partial differential equation (SPDEs) to the setting of SVIs. We also prove convergence of the numerical scheme to a probabilistically strong solution in probability if pathwise uniqueness holds. We perform numerical simulations to illustrate the behavior of the proposed numerical scheme as well as its non-conforming variant in the context of image denoising.
Keywords (deu)
Stochastic partial differential equations
Subject (eng)
ÖFOS 2012 -- 101 -- Mathematics
Type (eng)
lecture
Language
[eng]
Persistent identifier
https://phaidra.univie.ac.at/o:2064212
Date created
2024-02-14
Place of creation (eng)
ESI
Duration
42 minutes 33 seconds
Association (eng)
Research Platform Erwin Schrödinger International Institute for Mathematical Physics (ESI)
License
All rights reserved