We prove that an averaging principle holds for a general class of stochastic reaction-diffusion systems, having unbounded multiplicative noise, in any space dimension. We show that the classical Khasminskii approach for systems with a finite number of degrees of freedom can be extended to infinite-dimensional systems.
A Khasminskii type averaging principle for stochastic reaction-diffusion equations / S. CERRAI. - In: THE ANNALS OF APPLIED PROBABILITY. - ISSN 1050-5164. - STAMPA. - 19:(2009), pp. 899-948. [10.1214/08-AAP560]
A Khasminskii type averaging principle for stochastic reaction-diffusion equations
CERRAI, SANDRA
2009
Abstract
We prove that an averaging principle holds for a general class of stochastic reaction-diffusion systems, having unbounded multiplicative noise, in any space dimension. We show that the classical Khasminskii approach for systems with a finite number of degrees of freedom can be extended to infinite-dimensional systems.
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