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Reachability Questions in Piecewise Deterministic Markov Processes
2003We formulate a stochastic hybrid system model that allows us to capture a class of Markov processes known as piecewise deterministic Markov processes (PDMPs). For this class of stochastic processes we formulate a probabilistic reachability problem. Basic properties of PDMPs are reviewed and used to show that the reachability question is indeed well ...
Manuela-Luminita Bujorianu, John Lygeros
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Piecewise Deterministic Markov Decision Processes
2011In this chapter we deal with optimization problems where the state process is a Piecewise Deterministic Markov Process. These processes evolve through random jumps at random time points while the behavior between jumps is governed by an ordinary differential equation. They form a general and important class of non-diffusions.
Nicole Bäuerle, Ulrich Rieder
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From piecewise deterministic to piecewise diffusion Markov processes
Proceedings of the 27th IEEE Conference on Decision and Control, 2003The author presents PD (piecewise deterministic) processes as pathwise unique solutions of an Ito stochastic differential equation (SDE), driven by a Poisson random measure. Since such an SDE permits the inclusion of diffusion, this approach leads to a large variety of piecewise diffusion Markov processes, represented by pathwise unique SDE solutions. >
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Reachability Estimates of Piecewise Deterministic Markov Processes
2022 13th Asian Control Conference (ASCC), 2022Tua Agustinus Tamba, Bin Hu 0014
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Continuous Average Control of Piecewise Deterministic Markov Processes
2013The intent of this book is to present recent results in the control theory for the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs). The book focuses mainly on the long run average cost criteria and extends to the PDMPs some well-known techniques related to discrete-time and continuous-time Markov decision
Costa, Oswaldo, Dufour, François
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Piecewise deterministic Markov process for condition-based imperfect maintenance models
Reliability Engineering and System Safety, 2023Xian Chen
exaly
A class of piecewise deterministic Markov processes
2001This paper introduces a new class of piecewise deterministic Markov processes generalizing those of \textit{M. H. A. Davies} [J. R. Stat. Soc., Ser. B 46, 353-388 (1984; Zbl 0565.60070)]. Those processes \(X\) share a certain property of loss of memory after a catastrophe: if \(X_s = y\) and some catastrophe has occured in \(]s, t]\) (i.e.
COLOMBO, GIOVANNI, DAI PRA, PAOLO
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