A simple proof of heavy tail estimates for affine type Lipschitz recursions

Dariusz Buraczewski and Ewa Damek

Stochastic Processes and their Applications, 2017, vol. 127, issue 2, 657-668

Abstract: We study the affine recursion Xn=AnXn−1+Bn where (An,Bn)∈R+×R is an i.i.d. sequence and recursions Xn=Φn(Xn−1) defined by Lipschitz transformations such that Φ(x)≥Ax+B. It is known that under appropriate hypotheses the stationary solution X has regularly varying tail, i.e. limt→∞tαP[X>t]=C. However positivity of C in general is either unknown or requires some additional involved arguments. In this paper we give a simple proof that C>0. This applies, in particular, to the case when Kesten–Goldie assumptions are satisfied.

Keywords: Random difference equations; Affine recursion; Iterated functions system; Lipschitz recursion; Heavy tails; Tail estimates (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spa.2016.06.022

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