球壳内的布朗运动的生命时

LIFETIME OF BROWNIAN MOTION IN A SPHERICAL SHELL

设D ={x :x∈Rd,a <|x| <b} ,d≥ 2 ;X ={Xt} t≥ 0 为D内的布朗运动 ,其中 {x :|x| =a}为反射壁 ,{x :|x| =b}为吸收壁 .用Tab 表示X的生命时 本文求出了Tab 的分布函数 .

Let D={x:x∈R d,a<|x|<b},d ≥2; X={X t} t≥ 0 be the Brownian motion in D , where { x:|x|=a} is a reflecting barrier and {x:|x|=b} is an absorbing barrier.Let T a b be the lifetime of X ,we compute the distribution function of T a b .