About quasi-renewal processes and quasi-regenerative processes

TL;DR

This paper explores quasi-renewal and quasi-regenerative processes, proposing a method to bound their convergence rates to stationarity in ergodic cases, with significant revisions and expansions.

Contribution

It introduces a new method for bounding convergence rates of quasi-renewal and quasi-regenerative processes to their stationary distribution.

Findings

Proposed a method for upper bounds on convergence rates.

Extended and corrected the original theoretical framework.

Applicable to ergodic processes with regenerative properties.

Abstract

We discuss the concepts of quasi-renewal and quasi-regenerative processes. We also propose a method for obtaining the upper bounds for the convergence rate of the distribution of a regenerative and quasi-regenerative process to a stationary distribution, if this process is ergodic. The second version of the text has been corrected and significantly expanded.