Fractional integrals of stationary processes and the central limit theorem

1976 ◽  
Vol 13 (4) ◽  
pp. 723-732 ◽  
Author(s):  
M. Rosenblatt
Keyword(s):  
Limit Theorems ◽  
Fractional Integral ◽  
Burgers Equation ◽  
Fractional Integrals ◽  
Stationary Processes ◽  
Singular Behavior ◽  
Mixing Processes ◽  
The Central Limit Theorem ◽  
Strongly Mixing ◽  
Strongly Mixing Processes

A class of limit theorems involving asymptotic normality is derived for stationary processes whose spectral density has a singular behavior near frequency zero. Generally these processes have ‘long-range dependence’ but are generated from strongly mixing processes by a fractional integral or derivative transformation. Some related remarks are made about random solutions of the Burgers equation.

Fractional integrals of stationary processes and the central limit theorem

1976 ◽  
Vol 13 (04) ◽  
pp. 723-732 ◽  
Author(s):  
M. Rosenblatt
Keyword(s):  
Limit Theorems ◽  
Fractional Integral ◽  
Burgers Equation ◽  
Fractional Integrals ◽  
Stationary Processes ◽  
Singular Behavior ◽  
Mixing Processes ◽  
The Central Limit Theorem ◽  
Strongly Mixing ◽  
Strongly Mixing Processes

A class of limit theorems involving asymptotic normality is derived for stationary processes whose spectral density has a singular behavior near frequency zero. Generally these processes have ‘long-range dependence’ but are generated from strongly mixing processes by a fractional integral or derivative transformation. Some related remarks are made about random solutions of the Burgers equation.

Finite state bilaterally deterministic strongly mixing processes

1996 ◽  
Vol 95 (1) ◽  
pp. 115-133 ◽  
Author(s):  
Robert M. Burton ◽  
Manfred Denker ◽  
Meir Smorodinsky
Keyword(s):  
Mixing Processes ◽  
Strongly Mixing ◽  
Finite State ◽  
Strongly Mixing Processes

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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