Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise

Details Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise

2008-01-09

arxiv.org/abs/0801.1443v4

Appl. Math. Optim. 61 (2010), 27-56

Mathematics

Probability

31 pages, published in Appl. Math. Optim

Scientific paper

10.1007/s00245-009-9072-2

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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