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Asymptotics of mean exit time for small perturbations of a stochastic process. (Chinese. English summary) Zbl 0922.60032

Summary: Small perturbations \(\{X^\varepsilon(t)\}\) of a stochastic process \(\{X(t)\}\) in \(R^d\) \((d\geq 1)\) are considered, where \(\{X(t)\}\) and \(\{X^\varepsilon(t)\}\) satisfy stochastic differential equations \(dX(t)=b(X(t), Z(t))dt\) and \(dX^\varepsilon(t)=b(X^\varepsilon(t),Z(t))dt+\varepsilon dB(t)\), respectively, and \(\{Z(t)\}\) is a finite state Markov process. Applying the large deviation method, the asymptotics of mean exit time for \(\{X^\varepsilon (t)\}\) as the perturbations tend to zero is obtained.

MSC:

60F10 Large deviations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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