Mixed empirical stochastic point processes in compact metric spaces. II. (Ukrainian, English) Zbl 1164.60350

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

Teor. Jmovirn. Mat. Stat. 75, 121-126 (2006); translation in Theory Probab. Math. Stat. 75, 19-145 (2007).

The authors investigate models of finite simple mixed empirical ordered marked point processes in compact metric spaces. It is assumed that the probability measure \(P_{x}\) is defined on state space \(X\); on the mark space \(K=[a,b]\subset\mathbb R^1\), the probability \(P_{k}\) is given; and an arbitrary trajectory of the ordered marked point process is obtained from population by simple random sampling without replacement. The notion of ordered marked point process with independent and one-position dependent marking is proposed. An example of such a process is presented.
[For part I, cf. ibid., 74, 98–107 (2006); translation in Theory Probab. Math. Stat. 74, 113–123 (2007; Zbl 1150.60381)]

Reviewer: Aleksandr D. Borisenko (Kyïv)

MSC:

60G15

Gaussian processes

Keywords:

mixed empirical stochastic point processes; compact metric spaces; ordered marked point processes; simple random sampling without replacement

Citations:

Zbl 1150.60381