角域上的条件布朗运动(Ⅰ)——生命时(英文)

CONDITIONED BROWNIAN MOTION IN AN ANGULAR DOMAIN (Ⅰ)——LIETIME

设A_m^d={(x^1,…,x^d)∈R^d,x^i>0,1≤i≤m≤d},称之为由m个d-1维坐标平面围成的角域。研究了无穷区域A_m^d中的条件布朗运动生命时的有限性及可积性。在一定条件下得到了该生命时有限及可积的充要条件。同时给出了A_m^d中终止布朗运动及调和函数的若干结果。

Suppose A_m^d={(x^1,…,x^d)∈R^d, x^i>0, 1≤i≤m≤d}, the angular do- main whose boundary is consisted of m (d-1)-dimension coordinative superplanes. The lifetimes of conditioned Brownian motions in A_m^d are investigated on topics such as its finiteness and integrability. Some preliminary rssults involved in killed Brownian motion and positive harmonic functions in A_m^d are also presented.