A class of piecewise deterministic Markov processes
A class of piecewise deterministic Markov processes
This paper introduces a new class of piecewise deterministic Markov processes generalizing those of \textit{M. H. A. Davies} [J. R. Stat. Soc., Ser. B 46, 353-388 (1984; Zbl 0565.60070)]. Those processes \(X\) share a certain property of loss of memory after a catastrophe: if \(X_s = y\) and some catastrophe has occured in \(]s, t]\) (i.e. the deterministic flow defining \(X\) in this interval has been perturbed), then the pair \((s,y)\) influences the conditional law of \(X_t\) only through the support. Existence, uniqueness, and several sample path properties of these new processes are discussed, as well as interesting applications to earthquake models.
- University of Padua Italy
- University of Verona Italy
order between probabilities, Applications of queueing theory (congestion, allocation, storage, traffic, etc.), Continuous-time Markov processes on general state spaces, Jump processes, jump processes, loss of memory
order between probabilities, Applications of queueing theory (congestion, allocation, storage, traffic, etc.), Continuous-time Markov processes on general state spaces, Jump processes, jump processes, loss of memory
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