一个随机过程的小扰动的平均越出时间估计

ASYMPTOTICS OF MEAN EXIT TIME FOR SMALL PERTURBATIONS OF A STOCHASTIC PROCESS

考虑Ｒｄ（ｄ≥１）上随机过程｛Ｘ（ｔ）｝的小扰动｛Ｘε（ｔ）｝，其中｛Ｘ（ｔ）｝和｛Ｘε（ｔ）｝分别满足随机微分方程ｄＸ（ｔ）＝ｂ（Ｘ（ｔ），Ｚ（ｔ））ｄｔ和ｄＸε（ｔ）＝ｂ（Ｘε（ｔ），Ｚ（ｔ））ｄｔ＋εｄＢ（ｔ），这里｛Ｚ（ｔ）｝是一个有限状态马氏过程．应用大偏差方法，给出了当扰动趋于零时，｛Ｘε（ｔ）｝的平均越出时间的渐近估计．

In this paper, small perturbations {X ε(t)} of a stochastic process {X(t)} in R d(d≥1) are considered, where {X(t)} and {X ε(t)} satisfy stochastic differential equations d X(t)=b(X(t),Z(t)) d t and d X ε(t)=b(X ε(t),Z(t)) d t+ε d B(t) , respectively, and { Z(t) } is a finite state Markov process. Applying the large deviation method, the asymptotics of mean exit time for {X ε(t)} as the perturbations tend to zero is obtained.