退化扩散过程小扰动的平均越出时间估计

THE MEAN EXIT TIME ESTIMATES FOR SMALL PERTURBATIONS OF DEGENERATE DIFFUSION PROCESS

本文研究了Rd（d>2）上的扩散过程｛XEt｝，它是Rd上退化扩散过程｛Xt｝的小随机扰动，其中｛Xt｝满足随机微分方程dXt=b（Xt）dt＋（Xt）odWt;｛Xεt｝满足随机微分方程dXεt=b（Xεt）dt＋（Xεt）odWt＋ε（Xεt）dBt，ε＞0通过构造辅助系统，给出了｛Xεt｝的Freidlin－Wentzell型的平均越出时间估计.

In this paper, we study the diffusion processes {Xt} in Rd (d>2), where {Xt} satisfy the stochastic differential equations dXεt = b (Xεt) dt +T (Xεt) o dWt + ε (Xεt) dBt, ε > 0. {Xεt} are small random perturbations of the degnnerate diffusion process {Xt}, which satisfies the stochastic differential equation dXt = b(Xt) dt + T(Xt) o dWt. By means of the auxiliary systems, we obtain the Freidlin-Wentzell mean exit time estimates of {Xεt}.