Limit theorems for measures of sections of random sets. (English. Ukrainian original) Zbl 0923.60054

Yurachkivs’kyj, A. P.

Theory Probab. Math. Stat. 56, 183-188 (1998); translation from Teor. Jmovirn. Mat. Stat. 56, 177-182 (1997).

A collection of random sets \(\Gamma_{ni}(\omega)=\{x:\chi_{ni} (x,\omega)=1\}\) is considered. The stochastic process \(\xi_n(t)\) which is conditional expectation of the product \(\prod_{i=1}^{[nt]}(1-\chi_{ni})\) is studied. The author proves weak convergence \(\xi_n \to e^{-Q}\) (a.s.), where \(Q\) is a continuous and increasing process. Some corollaries for expectations are obtained.

Reviewer: A.Ya.Olenko (Kyïv)

MSC:

60G57	Random measures
60D05	Geometric probability and stochastic geometry
60F17	Functional limit theorems; invariance principles

Keywords:

limit theorems; measures; random sets