On the range, local times and periodicity of random walk on an interval

TL;DR

This paper investigates the behavior of symmetric and asymmetric random walks on an interval, focusing on their range, local times, and periodicity at exit times, providing new asymptotic distribution results.

Contribution

It introduces new asymptotic distribution results for the range, local times, and periodicity of various types of random walks on an interval.

Findings

Asymptotic distributions for the range and local times are derived.

Results apply to symmetric, weakly asymmetric, and asymmetric random walks.

The study enhances understanding of exit behaviors in random walks on finite intervals.

Abstract

The range, local times, and periodicity of symmetric, weakly asymmetric and asymmetric random walks at the time of exit from a strip with $N$ locations are considered. Several results on asymptotic distributions are obtained.