关键词: 首次退出时间, 随机微分方程, 奇异摄动

Abstract: We considered the first exit time problem in diffusion model of chemical reaction. Firstly, we transformed the problem of stochastic differential equation into a boundary value problem of partial differential equation. Secondly, we used the coordinate transformation and asymptotic expansion of singular perturbation  to obtain the first order approximate solution. Finally, we gave the results combined with the asymptotic method of Laplace integral.

Key words: first exit time, stochastic differential equation, singular perturbation