On Markov--up processes and their recurrence properties

TL;DR

This paper introduces a new class of Markov up processes, analyzing their recurrence and ergodic properties to understand their long-term behavior under certain conditions.

Contribution

It proposes a simple model for Markov up processes and establishes conditions for their positive recurrence and ergodicity, advancing understanding of their dynamics.

Findings

Positive recurrence under specific conditions

Ergodic properties demonstrated

Model provides a basis for further analysis

Abstract

A simple model of the new notion of "Markov up" processes is proposed; its positive recurrence and ergodic properties are shown under the appropriate conditions.