Some properties of point random fields with non-random compensators. (Russian) Zbl 0647.60054

Rojtgarts, A. D.

Teor. Veroyatn. Mat. Stat., Kiev 36, 119-127 (1987).

The author considers two-parameter point processes, i.e. nondecreasing stepped random functions in \(R^ 2_+\) with jumps 0 or 1. He represents Ito’s formula for such processes and proves with its help that “thin” point two-parameter processes with nonrandom compensators are fields with independent increments. Then he gives a criterion for point processes in \(R^ 2_+\) to be Poisson.

Reviewer: Yu.S.Mishura

MSC:

60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)
60G60	Random fields
60H05	Stochastic integrals

Keywords:

two-parameter point processes; Ito’s formula; nonrandom compensators; independent increments