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

Berglund N, Gentz B (2013)
Electronic Journal Of Probability 18: 1-58.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor/in
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Abstract / Bemerkung
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 [6]. 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.
Stichworte
Stochastic partial differential equations; pitchfork bifurcation; transition time; exit problem; subexponential asymptotics; capacities; Galerkin approximation; Wentzell-Freidlin theory; large deviations; theory; potential; Kramers' law; metastability; parabolic equations; reaction-diffusion equations
Erscheinungsjahr
2013
Zeitschriftentitel
Electronic Journal Of Probability
Band
18
Seite(n)
1-58
ISSN
1083-6489
Page URI
https://pub.uni-bielefeld.de/record/2584698

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Berglund N, Gentz B. Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond. Electronic Journal Of Probability. 2013;18:1-58.
Berglund, N., & Gentz, B. (2013). Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond. Electronic Journal Of Probability, 18, 1-58. doi:10.1214/EJP.v18-1802
Berglund, N., and Gentz, B. (2013). Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond. Electronic Journal Of Probability 18, 1-58.
Berglund, N., & Gentz, B., 2013. Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond. Electronic Journal Of Probability, 18, p 1-58.
N. Berglund and B. Gentz, “Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond”, Electronic Journal Of Probability, vol. 18, 2013, pp. 1-58.
Berglund, N., Gentz, B.: Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond. Electronic Journal Of Probability. 18, 1-58 (2013).
Berglund, Nils, and Gentz, Barbara. “Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond”. Electronic Journal Of Probability 18 (2013): 1-58.