Iterated random functions and slowly varying tails

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Dyszewski, Piotr¹ 

[1] Uniwersytet Wroctawski, Inst Matemat, Plac Grunwaldzki 2-4, PL-50384 Wroclaw, Poland

关键词: Stochastic recursions;    Random difference equation;    Stationary distribution;    Subexponential distributions;   

DOI  :  10.1016/j.spa.2015.09.005

来源: Elsevier

【 摘 要 】

Consider a sequence of i.i.d. random Lipschitz functions {psi(n)}(n >= 0). Using this sequence we can define a Markov chain via the recursive formula Rn+1 = psi(n+1)(R-n). It is a well known fact that under some mild moment assumptions this Markov chain has a unique stationary distribution. We are interested in the tail behaviour of this distribution in the case when psi(0)(t) approximate to A(0)t + B-0. We will show that under subexponential assumptions on the random variable log(+) (A(0) boolean OR B-0) the tail asymptotic in question can be described using the integrated tail function of log(+) (A(0) boolean OR B-0). In particular we will obtain new results for the random difference equation Rn+1 = A(n+1) R-n + Bn+1. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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