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Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond


 
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1. Title Title of document Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond
 
2. Creator Author's name, affiliation, country Nils Berglund; University of Orléans; France
 
2. Creator Author's name, affiliation, country Barbara Gentz; University of Bielefeld; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) SPDEs; reaction-diffusion equations; metastability; Kramers' law; exit problem; transition time; large deviations; Wentzell-Freidlin theory; potential theory; capacities; Galerkin approximation; subexponential asymptotics; pitchfork bifurcation
 
3. Subject Subject classification 60H15; 35K57; 60J45; 37H20
 
4. Description Abstract

We prove a Kramers-type law for metastable transition times for a class of one-dimensional parabolic stochastic partial differential equations (SPDEs) with bistable potential. The expected transition time between local minima of the potential energy depends exponentially on the energy barrier to overcome, with an explicit prefactor related to functional determinants. Our results cover situations where the functional determinants vanish owing to a bifurcation, thereby rigorously proving the results of formal computations announced in a previous work. The proofs rely on a spectral Galerkin approximation of the SPDE by a finite-dimensional system, and on a potential-theoretic approach to the computation of transition times in finite dimension.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Deutsche Forschungsgemeinschaft (DFG)
 
7. Date (YYYY-MM-DD) 2013-02-16
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1802
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-1802
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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