Sample Module for the Wiener Process on a VC Class of R~d
LU CHUANRONG(Hangzhou University, Hangzhou, 310028)
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.
【CateGory Index】： O189