arXiv subjects

Sandra Cerrai

Publications and source records attributed to Sandra Cerrai.

39 records · Page 3Linked to original sources

arXiv2010

Fast transport asymptotics for stochastic RDEs with boundary noise

We consider a class of stochastic reaction-diffusion equations also having a stochastic perturbation on the boundary and we show that when the diffusion rate is much larger than the rate of reaction, it is possible to replace the SPDE by a suitable one-dimensional stochastic differential equation. This replacement is possible under the assumption of spectral gap for the diffusion and is a result of averaging in the fast spatial transport. We also study the fluctuations around the averaged motion.

math.PR↗

arXiv2008

A Khasminskii type averaging principle for stochastic reaction-diffusion equations

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.

math.PR↗

arXiv2008

Averaging principle for a class of stochastic reaction-diffusion equations

We consider the averaging principle for stochastic reaction-diffusion equations. Under some assumptions providing existence of a unique invariant measure of the fast motion with the frozen slow component, we calculate limiting slow motion. The study of solvability of Kolmogorov equations in Hilbert spaces and the analysis of regularity properties of solutions, allow to generalize the classical approach to finite-dimensional problems of this type in the case of SPDE's.

math.PR↗