Coupling with compensators

We propose two general methods for coupling marked point processes (MPPs) on the real half-line that are explicitly formulated in terms of (canonical) compensators. These couplings are related to several results in the literature as compensator bounds for the total variation distance between two MPPs and strong coupling of renewal processes. The coupling of two MPPs with different initial conditions but the same compensators will lead to finite coupling times if the compensator admits certain properties of regeneration or contractivity.