Xi, Fubao Asymptotics of mean exit time for small perturbations of a stochastic process. (Chinese. English summary) Zbl 0922.60032 Appl. Math., Ser. A (Chin. Ed.) 14, No. 1, 49-55 (1999). 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) Keywords:small perturbation; large deviation; exit time PDFBibTeX XMLCite \textit{F. Xi}, Appl. Math., Ser. A (Chin. Ed.) 14, No. 1, 49--55 (1999; Zbl 0922.60032)