On a theorem of Breiman and a class of random difference equations

Denis Denisov, Bert Zwart

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We consider the tail behavior of the product of two independent nonnegative random variables X and Y. Breiman (1965) has considered this problem, assuming that X is regularly varying with index ?? and that E\{Y??+??\} {\textless} ??? for some ?? {\textgreater} 0. We investigate when the condition on Y can be weakened and apply our findings to analyze a class of random difference equations.
    Original languageEnglish
    Pages (from-to)1031-1046
    Number of pages16
    JournalJournal of Applied Probability
    Volume44
    Issue number4
    DOIs
    Publication statusPublished - Dec 2007

    Keywords

    • subexponential distribution

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