scholarly journals Strong Large Deviation and Local Limit Theorems

1986 ◽  
Author(s):  
Narasinga R. Chaganty ◽  
Jayaram Sethuraman
Keyword(s):  
Limit Theorems ◽  
Large Deviation ◽  
Local Limit ◽  
Local Limit Theorems

scholarly journals Strong Large Deviation and Local Limit Theorems

1989 ◽  
Author(s):  
Narasinga R. Chaganty ◽  
Jayaram Sethuraman
Keyword(s):  
Limit Theorems ◽  
Large Deviation ◽  
Local Limit ◽  
Local Limit Theorems

scholarly journals Strong Large Deviation and Local Limit Theorems

1993 ◽  
Vol 21 (3) ◽  
pp. 1671-1690 ◽  
Author(s):  
Narasinga Rao Chaganty ◽  
Jayaram Sethuraman
Keyword(s):  
Limit Theorems ◽  
Large Deviation ◽  
Local Limit ◽  
Local Limit Theorems

scholarly journals Large deviation local limit theorems for ratio statistics

1990 ◽  
Vol 19 (11) ◽  
pp. 4083-4101
Author(s):  
Narasinga Rao Chaganty ◽  
Sanjeev Sabnis
Keyword(s):  
Limit Theorems ◽  
Large Deviation ◽  
Local Limit ◽  
Local Limit Theorems

scholarly journals Multidimensional large deviation local limit theorems

1986 ◽  
Vol 20 (2) ◽  
pp. 190-204 ◽  
Author(s):  
Narasinga R. Chaganty ◽  
J. Sethuraman
Keyword(s):  
Limit Theorems ◽  
Large Deviation ◽  
Local Limit ◽  
Local Limit Theorems

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.

Large deviations of generalized renewal process

2020 ◽  
Vol 30 (4) ◽  
pp. 215-241
Author(s):  
Gavriil A. Bakay ◽  
Aleksandr V. Shklyaev
Keyword(s):  
Large Deviations ◽  
Renewal Process ◽  
Limit Theorems ◽  
Local Limit ◽  
Asymptotic Formulas ◽  
Additive Functionals ◽  
Wide Range ◽  
Finite Markov Chains ◽  
Independent Identically Distributed ◽  
Local Limit Theorems

AbstractLet (ξ(i), η(i)) ∈ ℝd+1, 1 ≤ i < ∞, be independent identically distributed random vectors, η(i) be nonnegative random variables, the vector (ξ(1), η(1)) satisfy the Cramer condition. On the base of renewal process, NT = max{k : η(1) + … + η(k) ≤ T} we define the generalized renewal process ZT = $\begin{array}{} \sum_{i=1}^{N_T} \end{array}$ξ(i). Put IΔT(x) = {y ∈ ℝd : xj ≤ yj < xj + ΔT, j = 1, …, d}. We find asymptotic formulas for the probabilities P(ZT ∈ IΔT(x)) as ΔT → 0 and P(ZT = x) in non-lattice and arithmetic cases, respectively, in a wide range of x values, including normal, moderate, and large deviations. The analogous results were obtained for a process with delay in which the distribution of (ξ(1), η(1)) differs from the distribution on the other steps. Using these results, we prove local limit theorems for processes with regeneration and for additive functionals of finite Markov chains, including normal, moderate, and large deviations.

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