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.
Bibliographical noteFunding 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.
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- Hybrid systems
- Moment closure
- Power-law distributions