On the Limit Distributions Associated with Step-kind Boundary Problems

TL;DR

This paper derives the limiting distributions for the first-passage time of a random walk crossing a step-function boundary, providing insights into boundary problems in stochastic processes.

Contribution

It introduces new limiting distribution results for first-passage times in step-boundary problems for random walks with positive drift.

Findings

Derived explicit limiting distributions for first-passage times.

Extended boundary problem analysis to step-function boundaries.

Provides theoretical foundation for stochastic boundary crossing analysis.

Abstract

A random walk generated by a sum of independent identity distributed random variables with positive expectation is considered. The limiting distributions for the first- passage -time of a step-function boundary are derived.