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

Denis Denisov, Bert Zwart

Research output: Contribution to journalArticle

31 Citations (Scopus)

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 a and that E{Ya+e] < 8 for some e > 0. We investigate when the condition on Y can be weakened and apply our findings to analyze a class of random difference equations. © Applied Probability Trust 2007.

Original languageEnglish
Pages (from-to)1031-1046
Number of pages16
JournalJournal of Applied Probability
Volume44
Issue number4
DOIs
Publication statusPublished - Dec 2007

Keywords

  • Random difference equation
  • Regular variation
  • Subexponential distribution

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