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Piecewise deterministic Markov processes in biological models [PDF]
, 2015 We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to dispersal of biological systems, cell cycle models, gene expression ...
Rudnicki, Ryszard, Tyran-Kaminska, Marta
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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.
Julius, Agung, +2 more
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Algorithmic bisimulation for communicating piecewise deterministic Markov processes [PDF]
Proceedings of the 44th IEEE Conference on Decision and Control, 2005 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).
Schaft, Arjan van der, Strubbe, Stefan
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Communicating Piecewise Deterministic Markov Processes [PDF]
IFAC Proceedings Volumes, 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
Strubbe, S.N. +2 more
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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
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Piecewise deterministic Markov processes and their invariant measures [PDF]
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2021 Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which implies quantitative bounds on the total variation between the marginal distributions of the two processes.
Durmus, Alain +2 more
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Piecewise deterministic Markov process — recent results [PDF]
ESAIM: Proceedings, 2014 We give a short overview of recent results on a specific class of Markov process: the Piecewise Deterministic Markov Processes (PDMPs). We first recall the definition of these processes and give some general results. On more specific cases such as the TCP model or a model of switched vector fields, better results can be proved, especially as regards ...
Azaïs, Romain +4 more
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HYPE with stochastic events [PDF]
Electronic Proceedings in Theoretical Computer Science, 2011 The process algebra HYPE was recently proposed as a fine-grained modelling approach for capturing the behaviour of hybrid systems. In the original proposal, each flow or influence affecting a variable is modelled separately and the overall behaviour of ...
Luca Bortolussi +2 more
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On Computations in Renewal Risk Models—Analytical and Statistical Aspects
Risks, 2020 We discuss aspects of numerical methods for the computation of Gerber-Shiu or discounted penalty-functions in renewal risk models. We take an analytical point of view and link this function to a partial-integro-differential equation and propose a ...
Josef Anton Strini, Stefan Thonhauser
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Effects of delayed immune-response in tumor immune-system interplay [PDF]
Electronic Proceedings in Theoretical Computer Science, 2012 Tumors constitute a wide family of diseases kinetically characterized by the co-presence of multiple spatio-temporal scales. So, tumor cells ecologically interplay with other kind of cells, e.g. endothelial cells or immune system effectors, producing and
Alberto d'Onofrio +4 more
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