TY - JOUR
AB - 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.
AU - Berglund, Nils
AU - Gentz, Barbara
ID - 2584698
JF - Electronic Journal Of Probability
KW - Stochastic partial differential equations
KW - pitchfork bifurcation
KW - transition time
KW - exit problem
KW - subexponential asymptotics
KW - capacities
KW - Galerkin approximation
KW - Wentzell-Freidlin theory
KW - large deviations
KW - theory
KW - potential
KW - Kramers' law
KW - metastability
KW - parabolic equations
KW - reaction-diffusion equations
SN - 1083-6489
TI - Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond
VL - 18
ER -