Two-Limit Problems for Almost Semi-Continuous Processes Defined on a Markov Chain

TL;DR

This paper studies the behavior of almost semi-continuous processes on finite Markov chains, focusing on their exit distributions from finite intervals and exploring some process modifications.

Contribution

It introduces new analysis of exit distributions for almost semi-continuous processes on Markov chains and examines process modifications.

Findings

Derived distributions of exit functionals.

Analyzed effects of process modifications.

Provided theoretical insights into process behavior.

Abstract

We consider almost upper semi-continuous processes defined on a finite Markov chain. The distributions of the functionals associated with the exit from a finite interval are studied. We also consider some modification of these processes.