Sharpening of the convergence rate in the multidimensional local limit theorem with stable limiting law

1977 ◽  
Vol 16 (3) ◽  
pp. 320-325 ◽  
Author(s):  
J. J. Banys
Keyword(s):  
Limit Theorem ◽  
Convergence Rate ◽  
Local Limit Theorem ◽  
Local Limit

scholarly journals An improvement of convergence rate in the local limit theorem for integral-valued random variables

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tatpon Siripraparat ◽  
Kritsana Neammanee
Keyword(s):  
Limit Theorem ◽  
Convergence Rate ◽  
Local Limit Theorem ◽  
Random Variables ◽  
Local Limit ◽  
Independent Random Variables ◽  
Moment Condition ◽  
Formula One ◽  
Explicit Constant ◽  
Independent Integral

AbstractLet $X_{1}, X_{2}, \ldots , X_{n}$ X 1 , X 2 , … , X n be independent integral-valued random variables, and let $S_{n}=\sum_{j=1}^{n}X_{j}$ S n = ∑ j = 1 n X j . One of the interesting probabilities is the probability at a particular point, i.e., the density of $S_{n}$ S n . The theorem that gives the estimation of this probability is called the local limit theorem. This theorem can be useful in finance, biology, etc. Petrov (Sums of Independent Random Variables, 1975) gave the rate $O (\frac{1}{n} )$ O ( 1 n ) of the local limit theorem with finite third moment condition. Most of the bounds of convergence are usually defined with the symbol O. Giuliano Antonini and Weber (Bernoulli 23(4B):3268–3310, 2017) were the first who gave the explicit constant C of error bound $\frac{C}{\sqrt{n}}$ C n . In this paper, we improve the convergence rate and constants of error bounds in local limit theorem for $S_{n}$ S n . Our constants are less complicated than before, and thus easy to use.

On a Lower Bound for the Convergence Rate in a Local Limit Theorem

1986 ◽  
Vol 30 (4) ◽  
pp. 810-814 ◽  
Author(s):  
V. K. Matskyavichyus
Keyword(s):  
Limit Theorem ◽  
Lower Bound ◽  
Convergence Rate ◽  
Local Limit Theorem ◽  
Local Limit

On Convergence Rate in the Local Limit Theorem for Densities*

2015 ◽  
Vol 205 (1) ◽  
pp. 105-112 ◽  
Author(s):  
I. G. Shevtsova
Keyword(s):  
Limit Theorem ◽  
Convergence Rate ◽  
Local Limit Theorem ◽  
Local Limit

Estimate of convergence rate in local limit theorem for the particle number in spin systems

1993 ◽  
Vol 95 (3) ◽  
pp. 738-747
Author(s):  
B. S. Nakhapetyan ◽  
S. K. Pogosyan
Keyword(s):  
Limit Theorem ◽  
Convergence Rate ◽  
Particle Number ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Spin Systems ◽  
Estimate Of Convergence Rate

scholarly journals Central and Local Limit Theorems for Numbers of the Tribonacci Triangle

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 880
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Limit Theorems ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Constructive Proof ◽  
The Central Limit Theorem ◽  
Local Limit Theorems

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

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