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Pruitt’s Estimates in Banach Space

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  • Philip S. Griffin

    (Syracuse University)

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.

Suggested Citation

  • Philip S. Griffin, 2010. "Pruitt’s Estimates in Banach Space," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1092-1109, December.
    • Handle: RePEc:spr:jotpro:v:23:y:2010:i:4:d:10.1007_s10959-009-0250-6
    DOI: 10.1007/s10959-009-0250-6
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    References listed on IDEAS

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    1. R. A. Doney & R. A. Maller, 2007. "Almost Sure Relative Stability of the Overshoot of Power Law Boundaries," Journal of Theoretical Probability, Springer, vol. 20(1), pages 47-63, March.
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