Coupling with compensators
Two general methods for coupling marked point processes (MPPs) on the real half-line are proposed. The MPPs are explicitly formulated in terms of (canonical) compensators, i.e. there is a (predictable in the canonical sense) kernel \(\alpha \) from \(S\times N_{\mathcal {X}}\) to \(R^{+} \times \mathcal {X}\), where \(S\) is the space of initial values, \(N_{\mathcal {X}}\) is the set of all possible realizations of the MPP with the mark space \(\mathcal {X}\). Coupling is a device used to establish convergence of stochastic processes. The main aim of the present paper is to prove the following property of ``weak ergodicity'': the total variance distance between time-shifted processes with the same compensator (but possibly different initial conditions) tends to zero.
scientific article; zbMATH DE number 1134794
scientific article