## Convergent numerical approximation of the stochastic total variation flow

Banas L, Röckner M, Wilke A (2020)
Stochastics and Partial Differential Equations : Analysis and Computations 9(2): 437-471.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Einrichtung
Abstract / Bemerkung
We study the stochastic total variation flow (STVF) equation with linear multiplicative noise. By considering a limit of a sequence of regularized stochastic gradient flows with respect to a regularization parameter we obtain the existence of a unique variational solution of the STVF equation which satisfies a stochastic variational inequality. We propose an energy preserving fully discrete finite element approximation for the regularized gradient flow equation and show that the numerical solution converges to the solution of the unregularized STVF equation. We perform numerical experiments to demonstrate the practicability of the proposed numerical approximation.
Stichworte
Stochastic variational inequalities; Convergent numerical approximation; Finite element method; Stochastic total variation flow; Image processing
Erscheinungsjahr
2020
Zeitschriftentitel
Stochastics and Partial Differential Equations : Analysis and Computations
Band
9
Ausgabe
2
Seite(n)
437-471
ISSN
2194-0401
eISSN
2194-041X
Page URI
https://pub.uni-bielefeld.de/record/2942720

## Zitieren

Banas L, Röckner M, Wilke A. Convergent numerical approximation of the stochastic total variation flow. Stochastics and Partial Differential Equations : Analysis and Computations . 2020;9(2):437-471.
Banas, L., Röckner, M., & Wilke, A. (2020). Convergent numerical approximation of the stochastic total variation flow. Stochastics and Partial Differential Equations : Analysis and Computations , 9(2), 437-471. https://doi.org/10.1007/s40072-020-00169-4
Banas, Lubomir, Röckner, Michael, and Wilke, Andre. 2020. “Convergent numerical approximation of the stochastic total variation flow”. Stochastics and Partial Differential Equations : Analysis and Computations 9 (2): 437-471.
Banas, L., Röckner, M., and Wilke, A. (2020). Convergent numerical approximation of the stochastic total variation flow. Stochastics and Partial Differential Equations : Analysis and Computations 9, 437-471.
Banas, L., Röckner, M., & Wilke, A., 2020. Convergent numerical approximation of the stochastic total variation flow. Stochastics and Partial Differential Equations : Analysis and Computations , 9(2), p 437-471.
L. Banas, M. Röckner, and A. Wilke, “Convergent numerical approximation of the stochastic total variation flow”, Stochastics and Partial Differential Equations : Analysis and Computations , vol. 9, 2020, pp. 437-471.
Banas, L., Röckner, M., Wilke, A.: Convergent numerical approximation of the stochastic total variation flow. Stochastics and Partial Differential Equations : Analysis and Computations . 9, 437-471 (2020).
Banas, Lubomir, Röckner, Michael, and Wilke, Andre. “Convergent numerical approximation of the stochastic total variation flow”. Stochastics and Partial Differential Equations : Analysis and Computations 9.2 (2020): 437-471.
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