Vol. 7, No. 4, 2014

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 4, 541–720
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
Cover Page
Editorial Board
Editors’ Addresses
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Subscriptions
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Invariant measures for hybrid stochastic systems

Xavier Garcia, Jennifer Kunze, Thomas Rudelius, Anthony Sanchez, Sijing Shao, Emily Speranza and Chad Vidden

Vol. 7 (2014), No. 4, 565–583
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.

Keywords
dynamical systems, Markov processes, Markov chains, stochastic modeling
Mathematical Subject Classification 2010
Primary: 34F05, 60J20, 37N20
Milestones
Received: 16 July 2013
Accepted: 5 October 2013
Published: 31 May 2014

Communicated by David Royal Larson
Authors
Xavier Garcia
Department of Mathematics
University of Minnesota
Minneapolis, MN 55455
United States
Jennifer Kunze
Mathematics and Computer Science Department
St. Mary’s College of Maryland
St. Mary’s City, MD 20686
United States
Thomas Rudelius
Department of Mathematics
Cornell University
Ithaca, NY 14850
United States
Anthony Sanchez
School of Mathematical and Statistical Sciences
Arizona State University
Tempe, AZ 85287-1804
United States
Sijing Shao
Department of Mathematics
Iowa State University
Ames, IA 50011
United States
Emily Speranza
Department of Mathematics, Engineering, and Computer Science
Carroll College
Helena, MT 59625
United States
Chad Vidden
Department of Mathematics
Iowa State University
Ames, IA 50011
United States