Poissons theorem

Celem pracy jest przedstawienie trzech najczęściej stosowanych metod dowodzenia twierdzenia Poissona dla zależnych zmiennych losowych.

The authors present three methods for proving Poisson's theorem. The first method is based on papers of L. Takács [J. Amer. Statist. Assoc. 62 (1967), 102–113; MR0217832] and J. Galambos [J. Appl. Probab. 11 (1974), 219–222; MR0358923], the second uses results of D. A. Freedman [Ann. Probab. 2 (1974), 256–269; MR0370694] and M. R. Leadbetter [Z. Wahrsch. Verw. Gebiete 28 (1973/74), 298–309; MR0362465], and the third method follows the considerations contained in another paper by Galambos [ibid. 32 (1975), no. 3, 197–207; MR0380941]. The paper contains known theorems but some of the proofs are new.