Electronic Journal of Probability

Well-Posedness and Asymptotic Behavior for Stochastic Reaction-Diffusion Equations with Multiplicative Poisson Noise

Carlo Marinelli and Michael Roeckner

Full-text: Open access

Abstract

We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations with a polynomially growing quasi-monotone nonlinearity and multiplicative Poisson noise. We also study existence and uniqueness of invariant measures for the associated semigroup in the Markovian case. A key role is played by a new maximal inequality for stochastic convolutions in $L_p$ spaces.

Article information

Source
Electron. J. Probab., Volume 15 (2010), paper no. 49, 1529-1555.

Dates
Accepted: 15 October 2010
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819834

Digital Object Identifier
doi:10.1214/EJP.v15-818

Mathematical Reviews number (MathSciNet)
MR2727320

Zentralblatt MATH identifier
1225.60108

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 60G57: Random measures

Keywords
Stochastic PDE reaction-diffusion equations Poisson measures monotone operators

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Marinelli, Carlo; Roeckner, Michael. Well-Posedness and Asymptotic Behavior for Stochastic Reaction-Diffusion Equations with Multiplicative Poisson Noise. Electron. J. Probab. 15 (2010), paper no. 49, 1529--1555. doi:10.1214/EJP.v15-818. https://projecteuclid.org/euclid.ejp/1464819834


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