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

1971 ◽  
Vol 11 (3) ◽  
pp. 627-639
Author(s):  
A. Mitalauskas
Keyword(s):  
Limit Theorem ◽  
Remainder Term ◽  
Stable Law ◽  
Integral Limit ◽  
Integral Limit Theorem

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

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

1969 ◽  
Vol 9 (4) ◽  
pp. 731-739
Author(s):  
J. Banys
Keyword(s):  
Limit Theorem ◽  
Remainder Term ◽  
Stable Limit ◽  
Integral Limit ◽  
Integral Limit Theorem ◽  
Multidimensional Integral

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

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

2006 ◽  
Vol 2006 ◽  
pp. 1-12
Author(s):  
Yuri P. Virchenko ◽  
M. I. Yastrubenko
Keyword(s):  
Limit Theorem ◽  
Random Number ◽  
First Passage ◽  
Integral Limit ◽  
Integral Limit Theorem ◽  
The Given ◽  
First Time ◽  
Mutually Independent ◽  
First Passage Problem ◽  
Independent Lattice

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.

A central limit theorem by remainder term for renewal processes

1992 ◽  
Vol 24 (2) ◽  
pp. 267-287 ◽  
Author(s):  
Allen L. Roginsky
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Renewal Processes

Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a remainder term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).

Sign in / Sign up

Export Citation Format

Share Document