一类高斯过程的碰撞概率  

Hitting Probabilities for a Class of Gaussian Processes

作　　者：朱燕芹 倪文清[1] ZHU Yanqin;NI Wenqing(School of Science,Jimei University,Xiamen 361021,China)

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《集美大学学报（自然科学版）》2024年第6期488-494,共7页Journal of Jimei University：Natural Science

基　　金：福建省中青年教师教育科研基金项目“各向异性随机场的几何性质及其应用”(JAT210228);集美大学科研基金资助项目“各向异性随机场轨道的分形性质及应用”(ZP2022014)。

摘　　要：令X={X(t),t∈R}是由X(t)=(X_(1)(t),…,X_(d)(t))(■_(t)∈R)定义在R_(d)上的高斯过程,其中X_(1),…,X_(d)独立同分布于一个实值高斯过程X_(0)={X_(0)(t),t∈R},且E[(X_(0)(t)-X_(0)(s))^(2)]≈γ^(2)(t-s)(f≈g表示存在常数c,使得c^(-1)g≤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。Let X={X(t),t∈R}be a Gaussian process with values in R^(d)defined by X(t)=(X_(1)(t),…,X_(d)(t))(■_(t)∈R),where X_(1),…,X_(d)are independent copies of a real-valued Gaussian process X_(0)={X_(0)(t),t∈R}and E[(X_(0)(t)-X_(0)(s))^(2)]≈γ^(2)(t-s)(f≈g indicates that there is a constant c,such that c^(-1)g≤f≤cg),γis 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 ofγ.The Hausdorff measure of the upper bound is determined by the upper indicesα^(*)of the functionγ,and the capacity of lower bound by the lower indicesα_(*).

关 键 词：碰撞概率 高斯过程 容量 HAUSDORFF测度 上指数 下指数 

分 类 号：O211.6[理学—概率论与数理统计]