Large deviation estimates for exceedance times of perpetuity sequences and their dual processes

• Published in: arXiv.org
• Main Authors: Buraczewski, Dariusz, Collamore, Jeffrey F, Damek, Ewa, Zienkiewicz, Jacek
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 27.11.2014
• Subjects: Asymptotic properties; Estimates

In a variety of problems in pure and applied probability, it is of relevant to study the large exceedance probabilities of the perpetuity sequence \(Y_n := B_1 + A_1 B_2 + \cdots + (A_1 \cdots A_{n-1}) B_n\), where \((A_i,B_i) \subset (0,\infty) \times {\mathbb R}\). Estimates for the stationary tai...