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January 2004 Large deviations for stochastic reaction-diffusion systems with multiplicative noise and non-Lipshitz reaction term
Sandra Cerrai, Michael Röckner
Ann. Probab. 32(1B): 1100-1139 (January 2004). DOI: 10.1214/aop/1079021473

Abstract

Following classical work by Freidlin [Trans. Amer. Math. Soc. (1988) 305 665--657] and subsequent works by Sowers [Ann. Probab. (1992) 20 504--537] and Peszat [Probab. Theory Related Fields (1994) 98 113--136], we prove large deviation estimates for the small noise limit of systems of stochastic reaction--diffusion equations with globally Lipschitz but unbounded diffusion coefficients, however, assuming the reaction terms to be only locally Lipschitz with polynomial growth. This generalizes results of the above mentioned authors. Our results apply, in particular, to systems of stochastic Ginzburg--Landau equations with multiplicative noise.

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Sandra Cerrai. Michael Röckner. "Large deviations for stochastic reaction-diffusion systems with multiplicative noise and non-Lipshitz reaction term." Ann. Probab. 32 (1B) 1100 - 1139, January 2004. https://doi.org/10.1214/aop/1079021473

Information

Published: January 2004
First available in Project Euclid: 11 March 2004

zbMATH: 1054.60065
MathSciNet: MR2044675
Digital Object Identifier: 10.1214/aop/1079021473

Subjects:
Primary: 60F10, 60H15

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 1B • January 2004
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