On almost sure noncentral limit theorems

1991 ◽  
Vol 4 (4) ◽  
pp. 767-781 ◽  
Author(s):  
Michael Lacey
Keyword(s):  
Limit Theorems ◽  
Noncentral Limit Theorems

scholarly journals Covariances Estimation for Long-Memory Processes

2010 ◽  
Vol 42 (1) ◽  
pp. 137-157 ◽  
Author(s):  
Wei Biao Wu ◽  
Yinxiao Huang ◽  
Wei Zheng
Keyword(s):  
Time Series ◽  
Asymptotic Behavior ◽  
Long Memory ◽  
Limit Theorems ◽  
Limiting Distribution ◽  
Linear Processes ◽  
Long Memory Processes ◽  
Noncentral Limit Theorems ◽  
Dependence Properties

For a time series, a plot of sample covariances is a popular way to assess its dependence properties. In this paper we give a systematic characterization of the asymptotic behavior of sample covariances of long-memory linear processes. Central and noncentral limit theorems are obtained for sample covariances with bounded as well as unbounded lags. It is shown that the limiting distribution depends in a very interesting way on the strength of dependence, the heavy-tailedness of the innovations, and the magnitude of the lags.

scholarly journals Covariances Estimation for Long-Memory Processes

2010 ◽  
Vol 42 (01) ◽  
pp. 137-157 ◽  
Author(s):  
Wei Biao Wu ◽  
Yinxiao Huang ◽  
Wei Zheng
Keyword(s):  
Time Series ◽  
Asymptotic Behavior ◽  
Long Memory ◽  
Limit Theorems ◽  
Limiting Distribution ◽  
Linear Processes ◽  
Long Memory Processes ◽  
Noncentral Limit Theorems ◽  
Dependence Properties

For a time series, a plot of sample covariances is a popular way to assess its dependence properties. In this paper we give a systematic characterization of the asymptotic behavior of sample covariances of long-memory linear processes. Central and noncentral limit theorems are obtained for sample covariances with bounded as well as unbounded lags. It is shown that the limiting distribution depends in a very interesting way on the strength of dependence, the heavy-tailedness of the innovations, and the magnitude of the lags.

scholarly journals Noncentral Limit Theorems and Appell Polynomials

1987 ◽  
Vol 15 (2) ◽  
pp. 767-775 ◽  
Author(s):  
Florin Avram ◽  
Murad S. Taqqu
Keyword(s):  
Limit Theorems ◽  
Appell Polynomials ◽  
Noncentral Limit Theorems

scholarly journals Central limit theorem for solutions of random initialized differential equations: a simple proof

2006 ◽  
Vol 2006 ◽  
pp. 1-20 ◽  
Author(s):  
Ileana Iribarren ◽  
José R. León
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Differential Equations ◽  
Gaussian Process ◽  
Simple Proof ◽  
Gaussian Measure ◽  
Limit Theorems ◽  
Integrable Function ◽  
Noncentral Limit Theorems ◽  
Square Integrable Function

We study the central and noncentral limit theorems for the convolution of a certain kernel h with F(ξ(⋅)), where ξ is a stationary Gaussian process and F is a square integrable function with respect to the standard Gaussian measure. Our method consists in showing that in the weak dependence case, we can use the Lindeberg method, approaching the initial Gaussian process by an m-dependent process. We could say that only variance computations are needed to get the two types of limits. Then we apply the obtained results to the solutions of the certain differential equations.

Limit theorems and price changes in financial markets

1998 ◽  
Vol 77 (5) ◽  
pp. 1353-1356
Author(s):  
Rosario N. Mantegna, H. Eugene Stanley
Keyword(s):  
Financial Markets ◽  
Limit Theorems ◽  
Price Changes

Limit theorems for long-memory flows on Wiener chaos

Bernoulli ◽  
2020 ◽  
Vol 26 (2) ◽  
pp. 1473-1503 ◽  
Author(s):  
Shuyang Bai ◽  
Murad S. Taqqu
Keyword(s):  
Long Memory ◽  
Limit Theorems ◽  
Wiener Chaos

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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