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《CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTIES》 1997-01
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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
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