Precise asymptotics for record times and the associated counting process

Allan Gut

Stochastic Processes and their Applications, 2002, vol. 101, issue 2, 233-239

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.

Keywords: i.i.d.; random; variables; Absolutely; continuous; Record; times; Counting; process; Strong; laws (search for similar items in EconPapers)
Date: 2002
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