Electronic Journal of Probability

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

Carlo Marinelli and Michael Roeckner

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Stochastic PDE reaction-diffusion equations Poisson measures monotone operators

This work is licensed under aCreative Commons Attribution 3.0 License.


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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