Well-posedness and asymptotic behavior for stochastic reaction-diffusion\n equations with multiplicative Poisson noise

2009/03/19 by Carlo Marinelli, Michael Röckner, Marinelli, Carlo +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0903.3299

openalex publication_date 2009/03/19 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28

Abstract

We establish well-posedness in the mild sense for a class of stochastic\nsemilinear evolution equations with a polynomially growing quasi-monotone\nnonlinearity and multiplicative Poisson noise. We also study existence and\nuniqueness of invariant measures for the associated semigroup in the Markovian\ncase. A key role is played by a new maximal inequality for stochastic\nconvolutions in L_p spaces.\n

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