REGULAR VARIATION IN THE TAIL BEHAVIOUR OF SOLUTIONS OF RANDOM DIFFERENCE EQUATIONS
成果类型：
Article
署名作者：
Grey, D. R.
署名单位：
University of Sheffield
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177005205
发表日期：
1994
页码：
169-183
关键词：
摘要：
Let Q and M be random variables with given joint distribution. Under some conditions Qn this joint distribution, there will be exactly one distribution for another random variable R, independent of (Q, M), with the property that Q + MR has the same distribution as R. When M is nonnegative and satisfies some moment conditions, we give an improved proof that if the upper tail of the distribution of Q is regularly varying, then the upper tail of the distribution of R behaves similarly; this proof also yields a converse. We also give an application to random environment branching processes, and consider extensions to cases where Q + MR is replaced by Psi(R) for random but nonlinear Psi and where M may be negative.