Piecewise deterministic Markov process — recent results
Copyright policy )Piecewise deterministic Markov process — recent results
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 long time behaviour. We continue our review with an infinite dimensional example of neuronal activity. From the statistical point of view, these models provide specific challenges: we illustrate this point with the example of the estimation of the distribution of the inter-jumping times. We conclude with a short overview on numerical methods used for simulating PDMPs.
- université de Rennes 1 France
- Sorbonne Paris Cité France
- UNIVERSITE DE MARNE LA VALLEE France
- Université de Rennes 1 France
- UNIVERSITE DE RENNES I France
switched vector fields, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Switched dynamical systems, ergodicity of Markov chains, Piecewise-deterministic Markov process, Mathematics - Statistics Theory, Statistics Theory (math.ST), 2010 Mathematics Subject Classification. Primary: 60J25, 510, Coupling, 62M05, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Discrete-time Markov processes on general state spaces, FOS: Mathematics, Wasserstein distance, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], Ergodicity, Probability (math.PR), numerical method, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], nonparametric estimation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 60J10 Secondary: 93E03,93E15,34D23, Continuous-time Markov processes on general state spaces, TCP model, Ergodicity., 60J75, Jump processes, piecewise deterministic Markov processes, Mathematics - Probability
switched vector fields, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Switched dynamical systems, ergodicity of Markov chains, Piecewise-deterministic Markov process, Mathematics - Statistics Theory, Statistics Theory (math.ST), 2010 Mathematics Subject Classification. Primary: 60J25, 510, Coupling, 62M05, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Discrete-time Markov processes on general state spaces, FOS: Mathematics, Wasserstein distance, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], Ergodicity, Probability (math.PR), numerical method, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], nonparametric estimation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 60J10 Secondary: 93E03,93E15,34D23, Continuous-time Markov processes on general state spaces, TCP model, Ergodicity., 60J75, Jump processes, piecewise deterministic Markov processes, Mathematics - Probability
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