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Communicating Piecewise Deterministic Markov Processes [PDF]

IFAC Proceedings Volumes, 2006
In this chapter we introduce the automata framework CPDP, which stands for Communicating Piecewise Deterministic Markov Processes. CPDP is developed for compositional modelling and analysis for a class of stochastic hybrid systems.
Strubbe, Stefan, Schaft, Arjan van der
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Piecewise deterministic Markov process - recent results [PDF]

ESAIM: Proceedings, 2014
Clermont-Ferrand, France, 29-31 August 2012We give a short overview of recent results on a specific class of Markov process: the Piecewise Deterministic Markov Processes (PDMPs).
Romain Azaïs, Krell, Nathalie, Pierre-andré Zitt, Alexandre Génadot, Azaïs, Romain, Jean-Baptiste Bardet, Jean-baptiste Bardet Alex, Bardet, Jean-Baptiste, Romain Azaïs, Zitt, Pierre-André, Nathalie Krell, Genadot, Alexandre, Re Génadot   +12 more
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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

Hypocoercivity of Piecewise Deterministic Markov Process-Monte Carlo [PDF]

The Annals of Applied Probability, 2021
International audienceIn this paper we derive spectral gap estimates for several Piecewise Deterministic Markov Processes, namely the Randomized Hamiltonian Monte Carlo, the Zig-Zag process and the Bouncy Particle Sampler. The hypocoercivity technique we
Durmus, Alain, Andrieu, Christophe, Nüsken, Nikolas, Roussel, Julien   +3 more
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On Risk-Sensitive Piecewise Deterministic Markov Decision Processes [PDF]

Applied Mathematics & Optimization, 2020
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.
Zhang, Yi; id_orcid, Guo, X, Guo, Xin, Zhang, Y   +3 more
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Change-point detection for Piecewise Deterministic Markov Processes [PDF]

Automatica, 2018
International audienceWe consider a change-point detection problem for a simple class of Piecewise Deterministic Markov Processes (PDMPs). A continuous-time PDMP is observed in discrete time and through noise, and the aim is to propose a numerical method
De Saporta, Benoîte, Cleynen, Alice
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Non-equilibrium Thermodynamics of Piecewise Deterministic Markov Processes

Journal of Statistical Physics, 2009
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states (x, σ) ∈ × , being a region in Rd or the d-dimensional torus, being a finite set.
FAGGIONATO A, RIBEZZI CRIVELLARI M., GABRIELLI, DAVIDE   +2 more
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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, Guillin, Arnaud, Monmarché, Pierre   +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
openaire   +5 more sources

Minimum contrast estimators for piecewise deterministic Markov processes

Numerical Algebra, Control and Optimization
International audienceThe main goal of this paper is to study the minimum contrast estimator (MCE) approach for the parameter estimation problem of piecewise deterministic Markov processes (PDMPs), associated to adaptive control problems.
Costa, Oswaldo Luiz Do Valle, Dufour, François, Genadot, Alexandre   +2 more
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