Variational solutions of stochastic partial differential equations with cylindrical Lévy noise

Tomasz Kosmala; Markus Riedle

doi:10.3934/dcdsb.2020209

Article Contents

2021, Volume 26, Issue 6: 2879-2898. Doi: 10.3934/dcdsb.2020209

This issue Previous Article Next Article Convergence rate of solutions toward stationary solutions to the isentropic micropolar fluid model in a half line

Variational solutions of stochastic partial differential equations with cylindrical Lévy noise

Tomasz Kosmala^1, and
Markus Riedle^2,3, ,

1.
School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK
2.
Department of Mathematics, King's College London, London WC2R 2LS, UK
3.
Institute of Mathematical Stochastics, Faculty of Mathematics, TU Dresden, 01062 Dresden, Germany

^* Corresponding author: Markus Riedle
^* Corresponding author: Markus Riedle

Received: November 30, 2019

Revised: March 31, 2020

Early access: July 2020

Published: June 2021

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Abstract

In this article, the existence of a unique solution in the variational approach of the stochastic evolution equation

$ \, \mathrm{d}X(t) = F(X(t)) \, \mathrm{d}t + G(X(t)) \, \mathrm{d}L(t) $

driven by a cylindrical Lévy process $ L $ is established. The coefficients $ F $ and $ G $ are assumed to satisfy the usual monotonicity and coercivity conditions. The noise is modelled by a cylindrical Lévy processes which is assumed to belong to a certain subclass of cylindrical Lévy processes and may not have finite moments.

Keywords:

cylindrical Lévy processes,
stochastic partial differential equations,
multiplicative noise,
variational solutions,
stochastic integration.

Mathematics Subject Classification: Primary: 60H15; Secondary: 60G51, 60G20, 28A35.

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