Coupling Poisson Processes by Self-Decomposability (original) (raw)

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 pm,n(s, t) of the pair (M (s), N(t)), 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.