Moment closure and finite-time blowup for piecewise deterministic markov processes

Lee DeVille, Sairaj Dhople, Alejandro D. Domínguez-García, Jiangmeng Zhang

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We present a variety of results analyzing the behavior of a class of stochastic processes-referred to as piecewise deterministic Markov processes (PDMPs)-for the infinite-time interval and determine general conditions on when the moments of such processes will, or will not, be well-behaved. We also characterize the types of finite-time blowups that are possible for these processes, and obtain bounds on their probabilities.

Original languageEnglish (US)
Pages (from-to)526-556
Number of pages31
JournalSIAM Journal on Applied Dynamical Systems
Volume15
Issue number1
DOIs
StatePublished - 2016

Bibliographical note

Funding Information:
This work was supported in part by the National Science Foundation (NSF) under awards ECCS-CAR-0954420, CMG-0934491, and CyberSEES-1442686; the Trustworthy Cyber Infrastructure for the Power Grid (TCIPG) under U.S. Department of Energy award DE-OE0000097; the National Aeronautics and Space Administration (NASA) through the NASA Astrobiology Institute under Cooperative Agreement NNA13AA91A issued through the Science Mission Directorate; and the Initiative for Mathematical Science and Engineering (IMSE) at the University of Illinois.

Publisher Copyright:
© Copyright 2016 SIAM.

Keywords

  • Hybrid systems
  • Moment closure
  • Power-law distributions

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