Two-parameter point random fields with nonrandom compensators. (English. Russian original) Zbl 0746.60057

Rojtgarts, A. D.

Theory Probab. Math. Stat. 42, 145-151 (1991); translation from Teor. Veroyatn. Mat. Stat., Kiev 42, 122-128 (1990).

It is well-known that a point process with non-random compensator is a process with independent increments. The author proves similar results for point fields defined in the plane. In this case there exist different types of compensators. One of the results: assume that the point field \(N\) has such a non-random increasing field \(A\) that \(N-A\) is a strong martingale. Then \(N\) is a field with independent increments. The characteristic function of \(N\) is also presented. It is proved that the finite-dimensional distributions of a point field with independent increments are uniquely determined by its non-random compensator.

Reviewer: Yu.S.Mishura (Kiev)

MSC:

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

Keywords:

point process; compensator; different types of compensators; characteristic function; point field with independent increments