Estimate of the speed of convergence in an integral limit theorem for multiplicative functions

1980 ◽  
Vol 20 (1) ◽  
pp. 25-33
Author(s):  
Z. Kryžius
Keyword(s):  
Limit Theorem ◽  
Speed Of Convergence ◽  
Multiplicative Functions ◽  
Integral Limit ◽  
Integral Limit Theorem

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 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 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.

Integral Limit Laws for Additive Functions

1973 ◽  
Vol 25 (1) ◽  
pp. 194-203
Author(s):  
J. Galambos
Keyword(s):  
Characteristic Function ◽  
Fourier Transforms ◽  
Mean Value ◽  
Characteristic Functions ◽  
Asymptotic Formulas ◽  
Mean Value Theorem ◽  
Multiplicative Functions ◽  
Additive Functions ◽  
Limit Laws ◽  
Integral Limit

In the present paper a general form of integral limit laws for additive functions is obtained. Our limit law contains Kubilius’ results [5] on his class H. In the proof we make use of characteristic functions (Fourier transforms), which reduces our problem to finding asymptotic formulas for sums of multiplicative functions. This requires an extension of previous results in order to enable us to take into consideration the parameter of the characteristic function in question. We call this extension a parametric mean value theorem for multiplicative functions and its proof is analytic on the line of [4].

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