Generalisation of the Eyring-Kramers transition rate formula to irreversible diffusion processes. (English) Zbl 1375.82081
The authors are dealing with the equilibrium systems which can be described by the overdamped diffusion of a particle in \(\mathbb R^d\) driven by the standard (Itô’s) stochastic differential equation. In such problems it is of interest to define the time scale at which transitions between different metastable states may occur. The Eyring-Kramers formula provides an answer for the Itô’s equation. Here the authors generalize this Eyring-Hramers formula for a more general class of stochastic differential equations referred to as Freidlin-Wentzell equation.
Reviewer: Guy Jumarie (Montréal)
MSC:
| 82C24 | Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics |
| 60J60 | Diffusion processes |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 60J65 | Brownian motion |
Keywords:
Eyring-Kramers formula; Freidlin-Wentzell theory; transport equation; stochastic differential equationReferences:
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