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arXiv · 1509.00629

Correlated Poisson processes and self-decomposable laws

Nicola Cufaro Petroni·Piergiacomo Sabino
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Abstract

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

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Nicola Cufaro Petroni, Piergiacomo Sabino. 2017-01-13. Correlated Poisson processes and self-decomposable laws. https://arxiv.org/abs/1509.00629

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