Capacities in Wiener space, quasi-sure lower functions, and Kolmogorov's [epsilon]-entropy

Davar Khoshnevisan, David A. Levin and Pedro J. Méndez-Hernández

Stochastic Processes and their Applications, 2008, vol. 118, issue 10, 1723-1737

Abstract: We propose a set-indexed family of capacities on the classical Wiener space . This family interpolates between the Wiener measure () on and the standard capacity () on Wiener space. We then apply our capacities to characterize all quasi-sure lower functions in . In order to do this we derive the following capacity estimate which may be of independent interest: There exists a constant a>1 such that for all r>0, Here, denotes the Kolmogorov [epsilon]-entropy of G, and f[small star, filled]:=sup[0,1]f.

Keywords: Capacity; in; Wiener; space; Lower; functions; Kolmogorov; entropy (search for similar items in EconPapers)
Date: 2008
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