Mixed empirical random point processes in compact metric spaces. I. (Ukrainian, English) Zbl 1150.60381

Petunin, Yu. I.; Semejko, M. G.

Teor. Jmovirn. Mat. Stat. 74, 98-107 (2006); translation in Theory Probab. Math. Stat. 74, 113-123 (2007).

This paper deals with the point processes and labelled point processes in a compact metric spaces, which are constructed on the samples obtained by simple random sampling without replacement from population. The structure of finite simple point processes and labelled point processes is investigated and notion of inducing sequence of probability measure of ordered point process is introduced. A model of finite simple mixed empirical ordered point process in compact metric space is constructed. The authors propose a family of multidimensional distributions, which completely defines the probability distribution of ordered point process.

Reviewer: Aleksandr D. Borisenko (Kyïv)

MSC:

60G55

Point processes (e.g., Poisson, Cox, Hawkes processes)

Keywords:

mixed empirical random point processes; compact metric spaces; labelled point processes