Small noise asymptotic expansions for stochastic PDE’s driven by dissipative nonlinearity and Lévy noise

Sergio Albeverio, Elisa Mastrogiacomo and Boubaker Smii

Stochastic Processes and their Applications, 2013, vol. 123, issue 6, 2084-2109

Abstract: We study a reaction–diffusion evolution equation perturbed by a space–time Lévy noise. The associated Kolmogorov operator is the sum of the infinitesimal generator of a C0-semigroup of strictly negative type acting on a Hilbert space and a nonlinear term which has at most polynomial growth, is non necessarily Lipschitz and is such that the whole system is dissipative.

Keywords: SPDEs; Dissipative systems; Lévy processes; Stochastic convolution with Lévy processes; Asymptotic expansions; Polynomially bounded nonlinearity; Stochastic FitzHugh–Nagumo system; Small noise; Lévy space time noise (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2013.01.013

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