Two nonrandom functional characteristics of random measure. (Ukrainian, English) Zbl 1026.60063

Yurachkivs’kyj, A. P.

Teor. Jmovirn. Mat. Stat. 65, 168-175 (2001); translation in Theory Probab. Math. Stat. 65, 189-197 (2002).

Let \(\psi\) be a random measure on a measurable space \((X,\mathcal X)\). The multiindex of the random measure \(\psi\) is defined as \[ \overline{\psi}(l;A_1,A_2,\dots)=\overline{\psi}^l(A_1,A_2,\dots)= E\prod_{j=1}^l{\psi}(A_j), \quad l\in{\mathbb N},\;A_j\in\mathcal X. \] In his articles [Theory Probab. Math. Stat. 60, 187-200 (2000); translation from Teor. Jmovirn. Mat. Stat. 60, 167-176 (1999; Zbl 0955.60051), Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 1999, No. 5, 49-54 (1999; Zbl 0962.60034) and Theory Stoch. Process. 5(21), No. 3-4, 242-257 (1999; Zbl 0993.60045)] the author introduced and studied a characteristic of a random measure which was called covaristic (covariation characteristic) function. The aim of this article is to find relations between the multiindex and the covaristic of a random measure similar to relations between the distribution function and the characteristic function of a random variable.

Reviewer: Mikhail Moklyachuk (Kyïv)

MSC:

60G57	Random measures
60D05	Geometric probability and stochastic geometry

Keywords:

random measure; covariation-characteristic function; distribution; multiindex

Citations:

Zbl 0955.60051; Zbl 0962.60034; Zbl 0993.60045