MOMENT STABILITY OF STOCHASTIC PROCESSES WITH APPLICATIONS TO CONTROL SYSTEMS

Document Type

Article

Publication Date

3-1-2024

Abstract

We establish new conditions for obtaining uniform bounds on the moments of discrete-time stochastic processes. Our results require a weak negative drift criterion along with a state-dependent restriction on the centered conditional moments of the process. They, in particular, generalize the main result of [22] which requires a constant bound on the averaged one-step jumps of the process. The state-dependent feature of our results make them suitable for a large class of multiplicative-noise processes. Under the additional assumption of the Markovian property, we prove new results on ergodicity that do not rely on a minorization condition typically needed in ergodic theorems. Several applications to iterative systems, control systems, and other dynamical systems with state-dependent multiplicative noise are included, and these illustrative examples demonstrate the wide applicability of our results.

Publication Source (Journal or Book title)

Mathematical Control and Related Fields

First Page

386

Last Page

412

This document is currently not available here.

Share

COinS