Martingales and first passage times of AR(1) sequences

TL;DR

This paper employs martingale methods to establish conditions for the exponential boundedness of first passage times in ergodic AR(1) sequences and derives explicit bounds for their expectations.

Contribution

It introduces a martingale identity and provides new sufficient conditions for exponential boundedness of first passage times in AR(1) processes.

Findings

Established sufficient conditions for exponential boundedness

Derived explicit bounds for first passage time expectations

Proved a martingale identity useful for analysis

Abstract

Using the martingale approach we find sufficient conditions for exponential boundedness of first passage times over a level for ergodic first order autoregressive sequences (AR(1)). Further, we prove a martingale identity to be used in obtaining explicit bounds for the expectation of first passage times.