Estimates for the distributions of the sums of subexponential random variables

V. Shneer

    Research output: Contribution to journalArticleAcademicpeer-review

    7 Citations (Scopus)


    Let be a random walk with independent identically distributed increments . We study the ratios of the probabilities P(S n >x) / P(1 > x) for all n and x. For some subclasses of subexponential distributions we find upper estimates uniform in x for the ratios which improve the available estimates for the whole class of subexponential distributions. We give some conditions sufficient for the asymptotic equivalence P(S > x) E P(1 > x) as x . Here is a positive integer-valued random variable independent of . The estimates obtained are also used to find the asymptotics of the tail distribution of the maximum of a random walk modulated by a regenerative process.
    Original languageEnglish
    Pages (from-to)1143-1158
    JournalSiberian Advances in Mathematics
    Issue number6
    Publication statusPublished - 2004


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