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- W2001340400 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. The corresponding Itô stochastic equation describes a process on a Hilbert space with dissipative nonlinear, non globally Lipschitz drift and a Lévy noise. Under smoothness assumptions on the nonlinearity, asymptotics to all orders in a small parameter in front of the noise are given, with detailed estimates on the remainders. Applications to nonlinear SPDEs with a linear term in the drift given by a Laplacian in a bounded domain are included. As a particular case we provide the small noise asymptotic expansions for the SPDE equations of FitzHugh–Nagumo type in neurobiology with external impulsive noise." @default.
- W2001340400 created "2016-06-24" @default.
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- W2001340400 date "2013-06-01" @default.
- W2001340400 modified "2023-09-27" @default.
- W2001340400 title "Small noise asymptotic expansions for stochastic PDE’s driven by dissipative nonlinearity and Lévy noise" @default.
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- W2001340400 doi "https://doi.org/10.1016/j.spa.2013.01.013" @default.
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