Random walk with equidistant multiple function barriers

TL;DR

This paper analyzes a discrete random walk on integers with regularly spaced barriers, deriving key probabilistic metrics such as expected arrivals, absorption probabilities, and absorption times.

Contribution

It introduces a novel analysis of random walks with multiple equidistant barriers, providing explicit formulas for various probabilistic measures.

Findings

Expected number of arrivals at barriers calculated

Absorption probabilities at different barriers derived

Expected time before absorption determined

Abstract

We obtain expected number of arrivals, absorption probabilities and expected time before absorption for a discrete random walk on the integers with an infinite set of equidistant multiple function barriers