Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise



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.


Stochastic evolution equation Large deviation principle Laplace principle Variational approach Weak convergence approach Reaction-diffusion equations Porous media equations Fast diffusion equations p-Laplace equation 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Fakultät Für MathematikUniversität BielefeldBielefeldGermany
  2. 2.School of Mathematical SciencesBeijing Normal UniversityBeijingChina

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