Small noise asymptotic expansions for stochastic PDE's, I. The case of a dissipative polynomially bounded nonlinearity

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概要

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• We study a reaction-diffusion evolution equation perturbed by a Gaussian noise. Here the leading operator is the infinitesimal generator of a $C_0$-semigroup of strictly negative type, the nonlinear term has at most polynomial growth and is such that the whole system is dissipative. The corresponding Ito stochastic equation describes a process on a Hilbert space with dissipative nonlinear, non globally Lipschitz drift and a Gaussian noise. Under smoothness assumptions on the nonlinearity, asymptotics to all orders in a small parameter in front of the noise are given, with uniform 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 example we consider the small noise asymptotic expansions for the stochastic FitzHugh-Nagumo equations of neurobiology around deterministic solutions.

著者

• Albeverio Sergio

  Institut Fur Mathematik Ruhr-universitat Bochum

• Di Persio

  Department Of Mathematics Nest Project University Of Trento

• Mastrogiacomo Elisa

  Dipartimento di Matematica F. Brioschi, Politecnico di Milano

• Mastrogiacomo Elisa

  Dipartimento Di Matematica F. Brioschi Politecnico Di Milano

• Albeverio Sergio

  Institute For Applied Mathematics University Of Bonn

関連論文

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• Small noise asymptotic expansions for stochastic PDE's, I. The case of a dissipative polynomially bounded nonlinearity

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