摘要
Brown运动是一个具有连续时间参数和连续状态空间的随机过程,有两种不同定义下的局部时,一种是P.Levy提出的"mesure du voisinage"的概念,也即Brown运动{Wt,Ft}t≥0的局部时Lt(x)=limε→014εmeas{0≤s≤t;|Ws-x|≤ε},t∈[0,∞),.x∈R.另一种是由游程理论定义的局部时lt(x),并给出这两种局部时之间的关系Lt(0)=24lt(0).
Brownian motion is a random process with continuous time parameter and continuous - state spaces. Two local times for Brownian motion under different definition are given. One isthe concept of ＂mesure du voisinage＂ proposed by P. Levy, represented as Lt（x）=limε→0 1/4ε meas{0≤s≤t;｜Ws-x｜≤ε},t∈[0,∞）,x∈R of {Wt,Ft}t≥0 Brownian motion. The other is lt （x） which is defined by excursion theory and shows the relationship between the two localtimes Lt（0）=√2/4lt（0）.
出处
《西安文理学院学报（自然科学版）》
2013年第1期36-38,共3页
Journal of Xi’an University(Natural Science Edition)
基金
河南软科学基金项目(2009A630026)
