On Stochastic Stability of a Class of non-Markovian Processes and Applications in Quantization

TL;DR

This paper investigates the stochastic stability of non-Markovian processes with stationary noise, exploring conditions for stationary measures, ergodicity, and applications in quantization and control systems.

Contribution

It introduces new stability analysis methods for non-Markovian processes and applies them to feedback quantization and stochastic control.

Findings

Established conditions for stationary measures in non-Markovian processes

Demonstrated ergodicity under certain stationarity assumptions

Applied results to feedback quantization systems

Abstract

In many applications, the common assumption that a driving noise process affecting a system is independent or Markovian may not be realistic, but the noise process may be assumed to be stationary. To study such problems, this paper investigates stochastic stability properties of a class of non-Markovian processes, where the existence of a stationary measure, asymptotic mean stationarity and ergodicity conditions are studied. Applications in feedback quantization and stochastic control are presented.