Maximal divergent uniform spacings

Ralph P. Russo and Mark D. Rothmann

Stochastic Processes and their Applications, 1989, vol. 33, issue 1, 175-183

Abstract: Let U1, U2,..., be a sequence of independent random variables, uniformly distributed on the unit interval, and let an, n[greater-or-equal, slanted]1, be an integer sequence for which 1[less-than-or-equals, slant]an[less-than-or-equals, slant]n. For n[greater-or-equal, slanted]1, define [Delta]n to be the largest of the an+1 spacings induced by the observations Un-an+1, Un-a n+2,...,Un.In this paper we consider the almost sure limiting behavior of the process [Delta]n, n[greater-or-equal, slanted]1.

Keywords: uniform; spacings; almost; sure; convergence; strong; laws; sample; path; properties (search for similar items in EconPapers)
Date: 1989
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