The integral limit theorem in the first passage problem for sums of independent nonnegative lattice variables

The integral limit theorem as to the probability distribution of the random numberνmof summands in the sum∑k=1νmξkis proved. Here,ξ1,ξ2,…are some nonnegative, mutually independent, lattice random variables being equally distributed andνmis defined by the condition that the sum value exceeds at the first time the given levelm∈ℕwhen the number of terms is equal toνm.

An estimate of the remainder term in the integral limit theorem in the case of convergence to the stable law

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: А. А. Миталаускас. Оценка остаточного члена в интегральной предельной теореме в случае сходимости к устойчивому закону A. Mitalauskas. Liekamojo nario įvertinimas integralinėje ribinėje teoremoje konvergavimo į stabilų dėsnį atveju

On the estimation of the remainder term in the multidimensional integral limit theorem for the stable limit law

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: И. И. Банис. Об оценке остаточного члена в многомерной интегральной предельной теореме при сходимости к устойчивому закону J Banys. Liekamojo nario įvertinimas daugiamatėje integralinėje ribinėje teoremoje stabilaus ribinio dėsnio atveju