Approximations of Piecewise Deterministic Markov Processes and their convergence properties [PDF]
Stochastic Processes and their Applications, 2021 Piecewise deterministic Markov processes (PDMPs) are a class of stochastic processes with applications in several fields of applied mathematics spanning from mathematical modeling of physical phenomena to computational methods.
Andrea Bertazzi, J. Bierkens, P. Dobson
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Continuous dependence of an invariant measure on the jump rate of a piecewise-deterministic Markov process. [PDF]
Mathematical biosciences and engineering : MBE, 2019 We investigate a piecewise-deterministic Markov process, evolving on a Polish metric space, whose deterministic behaviour between random jumps is governed by some semi-flow, and any state right after the jump is attained by a randomly selected continuous
D. Czapla +3 more
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A coordination model for ultra-large scale systems of systems [PDF]
Electronic Proceedings in Theoretical Computer Science, 2013 The ultra large multi-agent systems are becoming increasingly popular due to quick decay of the individual production costs and the potential of speeding up the solving of complex problems.
Manuela L. Bujorianu +1 more
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Ergodic properties of some piecewise-deterministic Markov process with application to gene expression modelling [PDF]
, 2017 A piecewise-deterministic Markov process, specified by random jumps and switching semi-flows, as well as the associated Markov chain given by its post-jump locations, are investigated in this paper.
D. Czapla +2 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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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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Piecewise Deterministic Markov Processes for Bayesian Neural Networks [PDF]
Conference on Uncertainty in Artificial Intelligence, 2023 Inference on modern Bayesian Neural Networks (BNNs) often relies on a variational inference treatment, imposing violated assumptions of independence and the form of the posterior.
Ethan Goan +3 more
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The law of the iterated logarithm for a piecewise deterministic Markov process assured by the properties of the Markov chain given by its post-jump locations [PDF]
Stochastic Analysis and Applications, 2019 In the paper, we consider some piecewise deterministic Markov process, whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process.
D. Czapla +3 more
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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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On level crossings for a general class of piecewise-deterministic Markov processes [PDF]
, 2007 We consider a piecewise-deterministic Markov process governed by a jump intensity function, a rate function that determines the behaviour between jumps, and a stochastic kernel describing the conditional distribution of jump sizes.
Borovkov, K. A., Last, G.
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