Iterated Piecewise-Stationary Random Functions

TL;DR

This paper extends the theory of iterated random functions to include time-varying distributions, providing bounds on tracking error for piecewise-stationary systems on Polish spaces, advancing understanding of uncertain dynamical systems.

Contribution

It introduces a novel framework for iterated random functions with time-varying distributions and proves new bounds on tracking error in this setting.

Findings

Established bounds on tracking error for piecewise-stationary random functions

Extended the theory to include time-varying distributions

Applicable to uncertain dynamical systems on Polish spaces

Abstract

Within the study of uncertain dynamical systems, iterated random functions are a key tool. There, one samples a family of functions according to a stationary distribution. Here, we introduce an extension, where one sample functions according to a time-varying distribution over the family of functions. For such iterated piecewise-stationary random functions on Polish spaces, we prove a number of results, including a bound on the tracking error.