Numerical approximation of probabilistically weak and strong solutions of the stochastic total variation flow

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F23%3A00571182" target="_blank" >RIV/67985556:_____/23:00571182 - isvavai.cz</a>
Result on the web
<a href="https://www.esaim-m2an.org/articles/m2an/abs/2023/02/m2an220087/m2an220087.html" target="_blank" >https://www.esaim-m2an.org/articles/m2an/abs/2023/02/m2an220087/m2an220087.html</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1051/m2an/2022089" target="_blank" >10.1051/m2an/2022089</a>

Result language
angličtina
Original language name
Numerical approximation of probabilistically weak and strong solutions of the stochastic total variation flow
Original language description
We propose a fully practical numerical scheme 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10103 - Statistics and probability

Project
<a href="/en/project/GA22-12790S" target="_blank" >GA22-12790S: Stochastic systems in infinite dimensions</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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