Iterated random functions and slowly varying tails

Piotr Dyszewski

Stochastic Processes and their Applications, 2016, vol. 126, issue 2, 392-413

Abstract: Consider a sequence of i.i.d. random Lipschitz functions {Ψn}n≥0. Using this sequence we can define a Markov chain via the recursive formula Rn+1=Ψn+1(Rn). 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 Ψ0(t)≈A0t+B0. We will show that under subexponential assumptions on the random variable log+(A0∨B0) the tail asymptotic in question can be described using the integrated tail function of log+(A0∨B0). In particular we will obtain new results for the random difference equation Rn+1=An+1Rn+Bn+1.

Keywords: Stochastic recursions; Random difference equation; Stationary distribution; Subexponential distributions (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spa.2015.09.005

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