Approximation of quasipotentials and exit problems for multidimensional RDE's with noise
Authors:
Sandra Cerrai and Mark Freidlin
Journal:
Trans. Amer. Math. Soc. 363 (2011), 38533892
MSC (2010):
Primary 60H15, 60F10, 35K57, 49J45
Published electronically:
February 10, 2011
MathSciNet review:
2775830
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Abstract: We deal with a class of reactiondiffusion equations, in space dimension , perturbed by a Gaussian noise which is white in time and colored in space. We assume that the noise has a small correlation radius , so that it converges to the white noise , as . By using arguments of convergence, we prove that, under suitable assumptions, the quasipotential converges to the quasipotential , corresponding to spacetime white noise, in spite of the fact that the equation perturbed by spacetime white noise has no solution. We apply these results to the asymptotic estimate of the mean of the exit time of the solution of the stochastic problem from a basin of attraction of an asymptotically stable point for the unperturbed problem.
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Additional Information
Sandra Cerrai
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742
Mark Freidlin
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742
DOI:
http://dx.doi.org/10.1090/S000299472011053523
PII:
S 00029947(2011)053523
Received by editor(s):
June 5, 2009
Received by editor(s) in revised form:
March 19, 2010
Published electronically:
February 10, 2011
Additional Notes:
The second author was partially supported by an NSF grant
Article copyright:
© Copyright 2011 American Mathematical Society
