A class of piecewise deterministic Markov processes (Q2758444)
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scientific article; zbMATH DE number 1679860
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A class of piecewise deterministic Markov processes |
scientific article; zbMATH DE number 1679860 |
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23 May 2002
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jump processes
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loss of memory
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order between probabilities
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0.96962404
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0.96597725
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0.95301324
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0.94490445
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0.9434587
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A class of piecewise deterministic Markov processes (English)
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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.
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