Moment stability of stochastic processes with applications to control systems
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 sizes of the one-step jumps of the processes. The state-dependent feature of the results make them suitable for a large class of multiplicative-noise processes. Under the additional assumption of Markovian property, new result on ergodicity has also been proved. There are several applications to iterative systems, control systems, and other dynamical systems with state-dependent multiplicative noise, and we include illustrative examples to demonstrate applicability of our results.
Keywords
Cite
@article{arxiv.2206.00200,
title = {Moment stability of stochastic processes with applications to control systems},
author = {Arnab Ganguly and Debasish Chatterjee},
journal= {arXiv preprint arXiv:2206.00200},
year = {2022}
}
Comments
23 pages. Theorem 2.2 of this article has some similarity in theme with the main result of a previous unpublished note of the authors, arXiv:1107.4749. But the setup of Theorem 2.2 is very different, and it has a much broader scope of applications. The rest of the article is entirely new