Stochastic recursions: Between Kesten's and Grincevicius-Grey's assumptions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Damek, Ewa¹  Kolodziejek, Bartosz² 

[1] Wroclaw Univ, Inst Math, Pl Grunwaldzki 2-4, PL-50384 Wroclaw, Poland

[2] Warsaw Univ Technol, Fac Math & Informat Sci, Koszykowa 75, PL-00662 Warsaw, Poland

关键词: Perturbed random walk;    Perpetuity;    Regular variation;    Renewal theory;   

DOI  :  10.1016/j.spa.2019.05.016

来源: Elsevier

【 摘 要 】

We study the stochastic recursion X-n = Psi(n)(Xn-1), where (Psi(n))(n >= 1) is a sequence of i.i.d. random Lipschitz mappings close to the random affine transformation x bar right arrow Ax + B. We describe the tail behaviour of the stationary solution X under the assumption that there exists alpha > 0 such that E vertical bar A vertical bar(alpha) = 1 and the tail of B is regularly varying with index -alpha < 0. We also find the second order asymptotics of the tail of X when Psi(x) = Ax + B. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free