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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
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 34F05, 60J20, 37N20
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Milestones
Received: 16 July 2013
Accepted: 5 October 2013
Published: 31 May 2014
Communicated by David Royal Larson
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Authors |
| Xavier Garcia | |
| Department of Mathematics University of Minnesota Minneapolis, MN 55455 United States |
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| Jennifer Kunze | |
| Mathematics and Computer Science
Department St. Mary’s College of Maryland St. Mary’s City, MD 20686 United States |
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| Thomas Rudelius | |
| Department of Mathematics Cornell University Ithaca, NY 14850 United States |
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| Anthony Sanchez | |
| School of Mathematical and
Statistical Sciences Arizona State University Tempe, AZ 85287-1804 United States |
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| Sijing Shao | |
| Department of Mathematics Iowa State University Ames, IA 50011 United States |
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| Emily Speranza | |
| Department of Mathematics,
Engineering, and Computer Science Carroll College Helena, MT 59625 United States |
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| Chad Vidden | |
| Department of Mathematics Iowa State University Ames, IA 50011 United States |
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