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First passage times for processes governed by master equations. (English) Zbl 0568.60071
Fluctuations and sensitivity in non-equilibrium systems, Proc. Int. Conf., Austin/Tex. 1984, Springer Proc. Phys. 1, 19-36 (1984).
[For the entire collection see Zbl 0565.00016.]
We calculate the activation rates of metastable states of processes governed by master equations, by calculating mean first passage times. We employ methods of singular perturbation theory to derive expressions for these rates, utilizing the full Kramers-Moyal expansions for the forward and backward operators in the master equation. In addition we discuss the validity of various diffusion approximations to the master equation, showing that such approximations are not valid in general.

MSC:
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
60H25 Random operators and equations (aspects of stochastic analysis)