Piecewise-Deterministic Markov Processes as Limits of Markov Jump Processes [PDF]
Advances in Applied Probability, 2012 A classical result about Markov jump processes states that a certain class of dynamical systems given by ordinary differential equations are obtained as the limit of a sequence of scaled Markov jump processes. This approach fails if the scaling cannot be carried out equally across all entities.
Franz, Uwe +2 more
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Monte Carlo filtering of piecewise deterministic processes [PDF]
, 2011 We present efficient Monte Carlo algorithms for performing Bayesian inference in a broad class of models: those in which the distributions of interest may be represented by time marginals of continuous-time jump processes conditional on a realisation of
Godsill, S +5 more
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Demographic noise and piecewise deterministic Markov processes [PDF]
Physical Review E, 2012 11 pages, 5 figures, minor ...
Realpe-Gomez, John +2 more
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Vasicek model with mixed-exponential jumps and its applications in finance and insurance
Advances in Difference Equations, 2018 In this paper, the authors study the distribution of the Vasicek model with mixed-exponential jumps and its applications in finance and insurance. With the aid of the piecewise deterministic Markov process theory and the martingale theory, the authors ...
Yongfeng Wu, Xue Liang
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Quantifying and Managing Uncertainty in Piecewise-Deterministic Markov Processes
SIAM/ASA Journal on Uncertainty Quantification, 2023 In piecewise-deterministic Markov processes (PDMPs) the state of a finite-dimensional system evolves continuously, but the evolutive equation may change randomly as a result of discrete switches. A running cost is integrated along the corresponding piecewise-deterministic trajectory up to the termination to produce the cumulative cost of the process ...
Elliot Cartee +4 more
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Multiscale Piecewise Deterministic Markov Process in infinite dimension: central limit theorem and Langevin approximation [PDF]
, 2014 In [A. Genadot and M. Thieullen, Averaging for a fully coupled piecewise-deterministic markov process in infinite dimensions. Adv. Appl. Probab. 44 (2012) 749–773], the authors addressed the question of averaging for a slow-fast
Thieullen, M. +3 more
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Applications of Stochastic Semigroups to Queueing Models
Annales Mathematicae Silesianae, 2019 Non-markovian queueing systems can be extended to piecewise-deterministic Markov processes by appending supplementary variables to the system. Then their analysis leads to an infinite system of partial differential equations with an infinite number of ...
Gwiżdż Piotr
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Fatigue Damage Mechanism-Based Dependent Modeling With Stochastic Degradation and Random Shocks
IEEE Access, 2018 This paper proposes a dependent modeling method for reliability estimation of metal structures under constant amplitude loading and random shocks considering the nonlinear damage accumulation mechanism.
Dan Xu +4 more
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Piecewise Deterministic Markov Processes in Biological Models [PDF]
, 2014 in: Semigroup of Operators - Theory and Applications, J. Banasiak et al. (eds.), Springer Proceedings in Mathematics & Statistics 113, (2015), pp.
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. 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
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