Small noise asymptotic expansions for stochastic PDE's. I: The case of a dissipative polynomially bounded non linearity

DOI10.2748/tmj/1325886292zbMath1234.35328OpenAlexW2046135257MaRDI QIDQ765682

Elisa Mastrogiacomo, Luca Di Persio, Sergio A. Albeverio

Publication date: 21 March 2012

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1325886292

zbMATH Keywords

asymptotic expansionsdissipative systemsreaction-diffusion equationsstochastic FitzHugh-Nagumo systempolynomially bounded nonlinearity

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Neural networks for/in biological studies, artificial life and related topics (92B20) Asymptotic expansions of solutions to PDEs (35C20) PDEs with randomness, stochastic partial differential equations (35R60)

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Along Paths Inspired by Ludwig Streit: Stochastic Equations for Quantum Fields and Related Systems ⋮ Precise Laplace asymptotics for singular stochastic PDEs: the case of 2D gPAM ⋮ A class of Lévy driven SDEs and their explicit invariant measures ⋮ Optimal control for the stochastic Fitzhugh-Nagumo model with recovery variable ⋮ Small noise asymptotic expansions for stochastic PDE's driven by dissipative nonlinearity and Lévy noise ⋮ Optimal control of the FitzHugh-Nagumo stochastic model with nonlinear diffusion ⋮ Diffusion processes in thin tubes and their limits on graphs ⋮ Asymptotic expansions for SDE's with small multiplicative noise ⋮ A representation of solutions to a scalar conservation law in several dimensions ⋮ Asymptotic expansion for some local volatility models arising in finance ⋮ Asymptotic expansion for a Black-Scholes model with small noise stochastic jump-diffusion interest rate

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