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Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise

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Abstract

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.

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Authors and Affiliations

  1. Fakultät Für Mathematik, Universität Bielefeld, 33501, Bielefeld, Germany

    Wei Liu

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Wei Liu

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  1. Wei Liu
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Correspondence to Wei Liu.

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Supported in part by the DFG through the Internationales Graduiertenkolleg “Stochastics and Real World Models” and NNSFC(10721091).

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Liu, W. Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise. Appl Math Optim 61, 27 (2010). https://doi.org/10.1007/s00245-009-9072-2

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