广义OUP_2奇点的蔓延

Propagation of Singularties in the Generalised Ornstein-uhlenbeckProcesses with Two Parameters

薛行雄讨论了OUP:关于重对数律的奇点可以沿水平方向和垂直方向蔓延的问题.张国楚引进了广义Browian Sheet和广义OUP_2概念.该文证明:在一定的条件下,广义OUP_2关于重对数律的奇点也可以沿水平、垂直方向蔓延.

: Let X(s,t) = g(s,t)[X + J(s,t)] be an generalized orustein-uhlenbeck Processes with two pa-rameters (GOUP2),where J(s,t) is a generalizesd Brown Shee (GBMP2). In this paper,we prove that each sec-tion Xc = X(s,c) is a GOUP1. We also discuss the law of iterated aloghthem of GOUP2. The results are moregeneral than that in work of Xie Xingxiong. A point (s,t) is called singularties of GOUP2, x(s,t,w) for fixed t ifH(s,t,w) = limsup | X(s + h,t) -X(s,t) |/ 1/h= + ∞. We point out that the sigularities can prop-agate parallelly to the coordinate axis under certain conditions just as in the Brownian Sheet.