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2013 Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond
Nils Berglund, Barbara Gentz
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Electron. J. Probab. 18: 1-58 (2013). DOI: 10.1214/EJP.v18-1802


<p>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.</p>


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Nils Berglund. Barbara Gentz. "Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond." Electron. J. Probab. 18 1 - 58, 2013.


Accepted: 16 February 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1285.60060
MathSciNet: MR3035752
Digital Object Identifier: 10.1214/EJP.v18-1802

Primary: 60H15
Secondary: 35K57 , 37H20 , 60J45

Keywords: Capacities , Exit problem , Galerkin approximation , Kramers' law , large deviations , metastability , Pitchfork bifurcation , potential theory , Reaction-diffusion equations , SPDEs , subexponential asymptotics , transition time , Wentzell-Freidlin theory

Vol.18 • 2013
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