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Communicating Piecewise Deterministic Markov Processes [PDF]
IFAC Postprint Volumes IPPV / International Federation of Automatic Control, 2003 Abstract In this paper we introduce CPDPs (Communicating Piecewise Deterministic Markov Processes) as an automata formalism for compositional specification of hybrid systems of the type PDP. A CPDP can be seen as an automaton representation of a PDP, with the extra possibility of interaction with other processes via a new concept that we call passive
A J Van Der Schaft
exaly +10 more sources
Approximation methods for piecewise deterministic Markov processes and their costs. [PDF]
Scand Actuar J, 2019 Scandinavian Actuarial Journal, 2019 (4)
Kritzer P +3 more
europepmc +8 more sources
Infinite dimensional Piecewise Deterministic Markov Processes
Stochastic Processes and their Applications, 2023 In this paper we aim to construct infinite dimensional versions of well established Piecewise Deterministic Monte Carlo methods, such as the Bouncy Particle Sampler, the Zig-Zag Sampler and the Boomerang Sampler. In order to do so we provide an abstract infinite-dimensional framework for Piecewise Deterministic Markov Processes (PDMPs) with unbounded ...
Paul Dobson, Joris Bierkens
core +7 more sources
Bisimulation for Communicating Piecewise Deterministic Markov Processes (CPDPs) [PDF]
, 2005 CPDPs (Communicating Piecewise Deterministic Markov Processes) can be used for compositional specification of systems from the class of stochastic hybrid processes formed by PDPs (Piecewise Deterministic Markov Processes). We define CPDPs and the composition of CPDPs, and prove that the class of CPDPs is closed under composition.
Strubbe, S.N., van der Schaft, Arjan
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Stochastic semantics for Communicating Piecewise Deterministic Markov Processes [PDF]
Proceedings of the 44th IEEE Conference on Decision and Control, 2006 CPDPs (Communicating Piecewise Deterministic Markov Processes) can be used for compositional specification of systems from the class of stochastic hybrid processes formed by PDPs (Piecewise Deterministic Markov Processes). We give an extension of the CPDP model.
Strubbe, S.N., van der Schaft, Arjan
core +5 more sources
Value passing for communicating piecewise deterministic Markov processes [PDF]
2006 American Control Conference, 2006 In this paper we extend the CPDP model, which is used for compositional specification of PDP-type stochastic hybrid systems, to the value passing CPDP model. With value passing we can express communication of values of continuous variables between CPDP components. We show that the class of value passing CPDPs is closed under composition.
Strubbe, Stefan +2 more
openaire +4 more sources
Numerical methods for piecewise deterministic Markov processes with boundary
ESAIM: Proceedings and Surveys, 2014 In this paper is described the general aspect of a numerical method for piecewise deterministic Markov processes with boundary. Under very natural hypotheses, a crucial result about uniqueness of solution of a generalized Kolmogorov ...
Goudenège Ludovic
doaj +4 more sources
Algorithmic bisimulation for Communicating Piecewise Deterministic Markov Processes [PDF]
Proceedings of the 44th IEEE Conference on Decision and Control, 2006 In this paper we present an algorithm for finding a bisimulation relation for stochastic hybrid systems from the class of CPDPs (Communicating Piecewise Deterministic Markov Processes). We prove that the fixed point of the algorithm forms a bisimulation on the state space of the CPDP.
Strubbe, S.N., van der Schaft, Arjan
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Supports of invariant measures for piecewise deterministic Markov processes [PDF]
Nonlinearity, 2017 For a class of piecewise deterministic Markov processes, the supports of the invariant measures are characterized. This is based on the analysis of controllability properties of an associated deterministic control system. Its invariant control sets determine the supports.
Benaïm, Michel +2 more
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On Risk-Sensitive Piecewise Deterministic Markov Decision Processes [PDF]
Applied Mathematics & Optimization, 2018 We consider a piecewise deterministic Markov decision process, where the expected exponential utility of total (nonnegative) cost is to be minimized. The cost rate, transition rate and post-jump distributions are under control. The state space is Borel, and the transition and cost rates are locally integrable along the drift.
Guo, Xin, Zhang, Yi
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