Time reversal of non-Markov point processes. (English) Zbl 0713.60061

Elliott, Robert J.; Tsoi, Allanus H.

Ann. Inst. Henri Poincaré, Probab. Stat. 26, No. 2, 357-373 (1990).

Time reversed forms of a standard Poisson process, a counting process with Markov intensity and that with predictable intensity are studied. In the first case, time reversal is considered with respect to the original measure, whereas in the latter two, with respect to an equivalently changed measure according to the intensity. It is shown that the time reversed processes are quasi-martingales and their representations in terms of the original processes are derived.

Reviewer: M.P.Jerschov

MSC:

60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)
60J75	Jump processes (MSC2010)
60G44	Martingales with continuous parameter

Keywords:

Poisson process; time reversed processes; quasi-martingales