Thickened renewal processes

R. A. Doney and George L. O'Brien

Stochastic Processes and their Applications, 1992, vol. 43, issue 1, 1-8

Abstract: Let {ti, i [greater-or-equal, slanted] 0} be an ordinary renewal process and assume the lifetime distribution function has the form F(x) = cx[alpha] (1 + [lambda]x + o(x)) near 0+. The asymptotic conditional distribution as n-->[infinity] of {nti, i[greater-or-equal, slanted]0}, given that tn [less-than-or-equals, slant] 1, is that of a renewal process with a gamma lifetime distribution depending only on [alpha].

Keywords: renewal; processes; conditioned; weak; limits; busy; periods (search for similar items in EconPapers)
Date: 1992
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