## Electronic Journal of Probability

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

#### Abstract

<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>

#### Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 24, 58 pp.

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

https://projecteuclid.org/euclid.ejp/1465064249

Digital Object Identifier
doi:10.1214/EJP.v18-1802

Mathematical Reviews number (MathSciNet)
MR3035752

Zentralblatt MATH identifier
1285.60060

Rights

#### Citation

Berglund, Nils; Gentz, Barbara. Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond. Electron. J. Probab. 18 (2013), paper no. 24, 58 pp. doi:10.1214/EJP.v18-1802. https://projecteuclid.org/euclid.ejp/1465064249

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