在R^d的VC类上Wiener测度的上界(英文)  

Sample Module for the Wiener Process on a VC Class of R^d

作　　者：陆传荣[1] 

机构地区：[1]杭州大学

出　　处：《应用概率统计》1997年第1期87-91,共5页Chinese Journal of Applied Probability and Statistics

摘　　要：本文考察指标集为d维欧氏空间Rd的子集类c的Wiener过程W的样本轨道性质．在某些情形中，对0＜an≤nd，an是不减的且an／nd是不增的假设下，求得函数Ψn使给出了Wiener测度在Rd的VC类的界，它也推广了Csorgo－Revesz关于Wiener过程增量的结果于这一一般情形．Sample path behavior is studied for the Wiener processes W indexed by classes C of subsetsof the Borel δ-field of Rd. For 0＜an ≤nd, an is nondecreasing and an/nd is nonmcreasing, afunction Ψn is found in some cases such that limsupn→∝sup｛|W(C(n))|/Ψn:C(n)∈C,|C(n)|≤an｝=1 a.s. This generalies the Csorgo-Revesz's increments results for a Wiener process.

关 键 词：集指标过程 上界 V-C类 维纳过程 维纳测度 

分 类 号：O211.62[理学—概率论与数理统计]