Stochastic recursions: Between Kesten’s and Grincevičius–Grey’s assumptions

Ewa Damek and Bartosz Kołodziejek

Stochastic Processes and their Applications, 2020, vol. 130, issue 3, 1792-1819

Abstract: We study the stochastic recursion Xn=Ψn(Xn−1), where (Ψn)n≥1 is a sequence of i.i.d. random Lipschitz mappings close to the random affine transformation x↦Ax+B. We describe the tail behaviour of the stationary solution X under the assumption that there exists α>0 such that E|A|α=1 and the tail of B is regularly varying with index −α<0. We also find the second order asymptotics of the tail of X when Ψ(x)=Ax+B.

Keywords: Perturbed random walk; Perpetuity; Regular variation; Renewal theory (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2019.05.016

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