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Precise asymptotics for record times and the associated counting process

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  • Gut, Allan

Abstract

Precise asymptotics have been proved for sums like [summation operator]n=1[infinity]nr/p-2P(Sn[greater-or-equal, slanted][var epsilon]n1/p) as [var epsilon][downward right arrow]0, where {Sn, n[greater-or-equal, slanted]1} are partial sums i.i.d. random variables, and, more recently, for renewal counting processes and first passage time processes of random walks. The present paper is devoted to analogous results for the record times and the associated counting process of i.i.d. absolutely continuous random variables.

Suggested Citation

  • Gut, Allan, 2002. "Precise asymptotics for record times and the associated counting process," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 233-239, October.
    • Handle: RePEc:eee:spapps:v:101:y:2002:i:2:p:233-239
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    References listed on IDEAS

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    1. Chen, Robert, 1978. "A remark on the tail probability of a distribution," Journal of Multivariate Analysis, Elsevier, vol. 8(2), pages 328-333, June.
    2. Gut, Allan, 1990. "Convergence rates for record times and the associated counting process," Stochastic Processes and their Applications, Elsevier, vol. 36(1), pages 135-151, October.
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