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Löpker and Palmowski have shown conditions under which a [[reversed process|time reversed]] PDMP is a PDMP.<ref>{{Cite journal | last1 = Löpker | first1 = A. | last2 = Palmowski | first2 = Z. | doi = 10.1214/EJP.v18-1958 | title = On time reversal of piecewise deterministic Markov processes | journal = Electronic Journal of Probability | volume = 18 | year = 2013 | arxiv = 1110.3813}}</ref> General conditions are known for PDMPs to be stable.<ref>{{Cite journal | last1 = Costa | first1 = O. L. V. | last2 = Dufour | first2 = F. | doi = 10.1137/060670109 | title = Stability and Ergodicity of Piecewise Deterministic Markov Processes | journal = SIAM Journal on Control and Optimization | volume = 47 | issue = 2 | pages = 1053 | year = 2008 | url = http://www.producao.usp.br/bitstream/BDPI/14708/1/art_COSTA_Stability_and_ergodicity_of_piecewise_deterministic_Markov_2008.pdf }}</ref>
Galtier and Al.<ref>{{Cite journal | last1 = Galtier | first1 = T. | doi = 10.1051/ps/2019015 | title =On the optimal importance process for piecewise deterministic Markov process | journal = ESAIM: PS | volume = 23 | year = 2019 }} </ref> studied the law of the trajectories of PDPM and provided a reference measure in order to express a '''density of a trajectory''' of the PDMP. Their work opens the way to any application using densities of trajectory. For instance, they used the density of a trajectories to perform importance sampling, this work was further developed by Chennetier and Al.<ref>{{Cite journal| last1 = Chennetier | first1 = G. | url = https://arxiv.org/pdf/2210.16185.pdf | title =Adaptive importance sampling based on fault tree analysis for piecewise deterministic Markov process | journal =preprint | year = 2022 }} </ref> to estimate the reliability of industrial systems.
==See also==
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