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

Author

Listed:
  • Khoshnevisan, Davar
  • Levin, David A.
  • Méndez-Hernández, Pedro J.

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.

Suggested Citation

  • Khoshnevisan, Davar & Levin, David A. & Méndez-Hernández, Pedro J., 2008. "Capacities in Wiener space, quasi-sure lower functions, and Kolmogorov's [epsilon]-entropy," Stochastic Processes and their Applications, Elsevier, vol. 118(10), pages 1723-1737, October.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:10:p:1723-1737
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