Invariant measures for hybrid stochastic systems

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 31 May 2014Embargo end date: 01 Jan 2014 English Publisher:Mathematical Sciences PublishersJournal:Involve, a Journal of Mathematics, volume 7, pages 565-583 (issn: 1944-4176, eissn: 1944-4184,

Copyright policy )

Authors: Garcia, Xavier; Kunze, Jennifer; Rudelius, Thomas; Sanchez, Anthony; Shao, Sijing; Speranza, Emily; Vidden, Chad;

doi: 10.2140/involve.2014.7.565 , 10.48550/arxiv.1408.0026

arXiv: 1408.0026

Invariant measures for hybrid stochastic systems

- Summary
- Subjects
- Metrics

Abstract

In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as time-homogeneous Markov processes. In particular, we prove the existence of invariant measures for each embedded system and relate the invariant measures for the various systems through the flow. We calculate these invariant measures explicitly in several illustrative examples.

18 pages, 7 figures

Related Organizations

Arizona State University
United States
University of Minnesota System
United States
University of Minnesota
United States
University of Minnesota
United States
University of Minnesota Morris
United States

View all View all

Keywords

Markov chains, Markov processes, Probability (math.PR), 37N20, Dynamical Systems (math.DS), dynamical systems, 34F05, FOS: Mathematics, 60J20, Mathematics - Dynamical Systems, Mathematics - Probability, stochastic modeling

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	0
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average