一类高斯过程的碰撞概率-《集美大学学报（自然科学版）》

文章信息/Info

Author(s):: ZHU Yanqin; NI Wenqing; School of Science,Jimei University,Xiamen 361021,China

Keywords:: hitting probabilities; Gaussian processes; capacity; Hausdorff measure; upper indices; lower indices

摘要:: 令X={X(t),t∈R是由X(t)=(X1(t),…,Xd(t))(t∈R)定义在Rd上的高斯过程,其中X1,…,Xd独立同分布于一个实值高斯过程X0={X0(t),t∈R},且E[(X0(t)-X0(s))2]≈γ2(|t-s|) (f≈g表示存在常数c,使得c-1g≤f≤cg)，γ是满足一定条件且具有上下指数的函数。利用γ的上下指数研究该过程碰撞概率,其上界的Hausdorff测度由γ的上指数α*确定,而下界的容量由下指数α*确定。

Abstract:: Let X={X(t),t∈R be a Gaussian process with values in Rddefined by X(t)=(X1(t),…,Xd(t))(t∈R),where X1,…,Xd are independent copies of a real-valued Gaussian process X0={X0(t),t∈R} and E[(X0(t)-X0(s))2]≈γ2(|t-s|) (f≈g indicates that there is a constant c,such that c-1g≤f≤cg)，γ is a function that satisfies certain conditions and has upper and lower indices.The purpose of this paper is to study the hitting probabilities of the process by using the upper and lower indices of γ.The Hausdorff measure of the upper bound is determined by the upper indices α*of the function γ，and the capacity of lower bound by the lower indices α*.