Random difference equations with subexponential innovations

Qi He Tang, Zhong Yi Yuan

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We consider the random difference equations S =d (X + S)Y and T =dX + TY, where =d denotes equality in distribution, X and Y are two nonnegative random variables, and S and T on the right-hand side are independent of (X, Y). Under the assumptions that X follows a subexponential distribution with a nonzero lower Karamata index, that Y takes values in [0, 1] and is not degenerate at 0 or 1, and that (X, Y) fulfills a certain dependence structure via the conditional tail probability of X given Y, we derive some asymptotic formulas for the tail probabilities of the weak solutions S and T to these equations. In doing so we also obtain some by-products which are interesting in their own right.

Original languageEnglish (US)
Pages (from-to)2411-2426
Number of pages16
JournalScience China Mathematics
Volume59
Issue number12
DOIs
StatePublished - Dec 1 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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