Pruitt's Estimates in Banach Space

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Abstract

Pruitt's estimates on the expectation and the distribution of the time taken by a random walk to exit a ball of radius r are extended to the infinite-dimensional setting. It is shown that they separate into two pairs of estimates depending on whether the space is type 2 or cotype 2. It is further shown that these estimates characterize type 2 and cotype 2 spaces.

Original languageEnglish (US)
Pages (from-to)1092-1109
Number of pages18
JournalJournal of Theoretical Probability
Volume23
Issue number4
DOIs
StatePublished - Dec 1 2010

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Keywords

  • Banach space
  • Cotype
  • Expected exit time
  • Probability estimates
  • Type

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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