ar X iv : m at h . PR / 0 70 19 20 v 2 21 F eb 2 00 7 On lower limits and equivalences for distribution tails of randomly stopped sums

نویسندگان

  • D. Denisov
  • S. Foss
  • D. Korshunov
چکیده

For a distribution F * τ of a random sum S τ = ξ 1 +. .. + ξ τ of i.i.d. random variables with a common distribution F on the half-line [0, ∞), we study the limits of the ratios of tails F * τ (x)/F (x) as x → ∞ (here τ is an independent counting random variable). We also consider applications of obtained results to random walks, compound Poisson distributions, infinitely divisible laws, and sub-critical branching processes. Let τ be a counting random variable which does not depend on {ξ n } n≥1 and has finite mean. Denote by F * τ the distribution of a randomly stopped sum S τ = ξ 1 +. .. + ξ τ. In this paper we discuss how does the tail behaviour of F * τ relate to that of F and, in particular, under what conditions

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DENIS DENISOV, SERGUEI FOSS and DMITRY KORSHUNOV Eurandom, P.O. Box 513 – 5600 MB Eindhoven, The Netherlands. School of MACS, Heriot-Watt University, Edinburgh EH14 4AS, UK. E-mail: [email protected]; [email protected] Sobolev Institute of Mathematics, 4 Koptyuga pr., Novosibirsk 630090, Russia. E-mail: [email protected] Novosibirsk State University, 2 Pirogova str., Novosibirsk 630090, Ru...

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تاریخ انتشار 2007