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Piecewise deterministic Markov processes and dynamic reliability

Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2008
If the reliability community remains interested in dynamic reliability theory, it is not really convinced by the ability of already available approaches to treating current problems from within the operational domain, even if the methodological quality of these approaches is undeniable.
Zhang, Huilong   +3 more
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Adaptive average control for piecewise deterministic Markov processes

Systems & Control Letters, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Costa, O.L.V.   +2 more
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Piecewise Deterministic Markov Decision Processes

2011
In 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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Safety Verification of Piecewise-Deterministic Markov Processes

Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control, 2016
We consider the safety problem of piecewise-deterministic Markov processes (PDMP). These are systems that have deterministic dynamics and stochastic jumps, where both the time and the destination of the jumps are stochastic. Specifically, we solve a p-safety problem, where we identify the set of initial states from which the probability to reach ...
Rafael Wisniewski   +3 more
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From piecewise deterministic to piecewise diffusion Markov processes

Proceedings of the 27th IEEE Conference on Decision and Control, 2003
The 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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Minimum contrast estimators for piecewise deterministic Markov processes

Numerical Algebra, Control and Optimization
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Costa, Oswaldo Luiz Do Valle   +2 more
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Continuous Average Control of Piecewise Deterministic Markov Processes

2013
The 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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Stationary distributions for piecewise-deterministic Markov processes

Journal of Applied Probability, 1990
In this paper we show that the problem of existence and uniqueness of stationary distributions for piecewise-deterministic Markov processes (PDPs) is equivalent to the same problem for the associated Markov chain, so long as some mild conditions on the parameters of the PDP are satisfied.
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Optimal control of piecewise deterministic markov process

Stochastics, 1985
The trajectories of piecewise deterministic Markov processes are solutions of an ordinary (vector)differential equation with possible random jumps between the different integral curves. Both continuous deterministic motion and the random jumps of the processes are controlled in order to minimize the expected value of a performance functional consisting
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