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 (M(s), N(t)), an outcome which turns out to be instrumental to produce explicit algorithms for future applications. We finally discuss the cross-correlation properties of the two processes and the relative timing of their jumps

Coupling Poisson processes by self-decomposability

CUFARO PETRONI, Nicola;SABINO, PIERGIACOMO
2017-01-01

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 (M(s), N(t)), an outcome which turns out to be instrumental to produce explicit algorithms for future applications. We finally discuss the cross-correlation properties of the two processes and the relative timing of their jumps
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/180468
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