Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise

Journal Article · Mon Feb 15 00:00:00 EST 2010 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-009-9072-2· OSTI ID:21480278

Liu Wei, E-mail: [e-mail].c ^[1]

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1. Universitaet Bielefeld, Fakultaet fuer Mathematik (Germany)

The Freidlin-Wentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. As examples, the main results are applied to derive the large deviation principle for different types of SPDE such as stochastic reaction-diffusion equations, stochastic porous media equations and fast diffusion equations, and the stochastic p-Laplace equation in Hilbert space. The weak convergence approach is employed in the proof to establish the Laplace principle, which is equivalent to the large deviation principle in our framework.

• OSTI ID: 21480278
• Journal Information: Applied Mathematics and Optimization, Vol. 61, Issue 1; Other Information: DOI: 10.1007/s00245-009-9072-2; Copyright (c) 2010 Springer Science+Business Media, LLC; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
CONVERGENCE
DIFFUSION EQUATIONS
HILBERT SPACE
LAPLACE EQUATION
MATHEMATICAL EVOLUTION
NOISE
STOCHASTIC PROCESSES
BANACH SPACE
DIFFERENTIAL EQUATIONS
EQUATIONS
EVOLUTION
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
SPACE