Limit theorem for first passage times in the random walk described by the generalization of the autoregressive process

Rahimov, F.H.; Ibadova, I.A.; Farhadova, AYNURƏ

doi:10.29229/uzmj.2020-4-11

Limit theorem for first passage times in the random walk described by the generalization of the autoregressive process

Rahimov F., Ibadova I., Farhadova A.

Uzbek Mathematical Journal, vol.64, no.4, pp.102-110, 2020 (Scopus)

Publication Type: Article / Article
Volume: 64 Issue: 4
Publication Date: 2020
Doi Number: 10.29229/uzmj.2020-4-11
Journal Name: Uzbek Mathematical Journal
Journal Indexes: Scopus
Page Numbers: pp.102-110
Keywords: autoregressive process of order one, central limit theorem, first passage time, Markov random walk
Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

In the paper we prove a central limit theorem for the family of the first passage times beyond a level by a perturbed Markov random walk described by a nonlinear function of the generalization of the autoregressive process of order one (AR (1)).