Sharp asymptotics of metastable transition times for one dimensional SPDEs

Details Sharp asymptotics of metastable transition times for one dimensional SPDEs Sharp asymptotics of metastable transition times for one dimensional SPDEs

2012-01-21

arxiv.org/abs/1201.4440v1

Mathematics

Probability

38 pages

Scientific paper

We consider a class of parabolic semi-linear stochastic partial differential equations driven by space-time white noise on a compact space interval. Our aim is to obtain precise asymptotics of the transition times between metastable states. A version of the so-called Eyring-Kramers Formula is proven in an infinite dimensional setting. The proof is based on a spatial finite difference discretization of the stochastic partial differential equation. The expected transition time is computed for the finite dimensional approximation and controlled uniformly in the dimension.

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