Correlated Poisson processes and self-decomposable laws
| Autor: | Petroni, Nicola Cufaro, Sabino, Piergiacomo |
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| Rok vydání: | 2015 |
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| Druh dokumentu: | Working Paper |
| Popis: | We analyze a method to produce pairs of non independent Poisson processes $M(t),N(t)$ from positively correlated, self-decomposable, exponential renewals. In particular the present paper provides the family of copulas pairing the renewals, along with the closed form for the joint distribution $p_{m,n}(s,t)$ of the pair $\big(M(s),N(t)\big)$, an outcome which turns out to be instrumental to produce explicit algorithms for applications in finance and queuing theory. We finally discuss the cross-correlation properties of the two processes and the relative timing of their jumps Comment: 45 pages; lengthy calculations in the appendices; 7 figures; in press on Med. J. Math |
| Databáze: | arXiv |
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