Coordinate point fields and their compensators. I. (English. Ukrainian original) Zbl 0923.60055

Mishura, Yu. S.

Theory Probab. Math. Stat. 55, 153-159 (1997); translation from Teor. Jmovirn. Mat. Stat. 55, 144-150 (1996).

Two-parameter point random fields are considered. Notions of predictable stopping set, weak predictable stopping set, strong martingale, and compensator are introduced and investigated for point random fields. Decompositions of random fields and compensators are proposed.

Reviewer: M.P.Moklyachuk (Kyïv)

MSC:

60G60	Random fields
60G44	Martingales with continuous parameter
60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)

Keywords:

random fields; compensator; martingale