Sums and maxima of discrete stationary processes

1993 ◽  
Vol 30 (04) ◽  
pp. 863-876 ◽  
Author(s):  
William P. McCormick ◽  
Jiayang Sun
Keyword(s):  
Asymptotic Behavior ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Stationary Processes ◽  
Limiting Behavior ◽  
Asymptotic Bounds

This paper considers the joint limiting behavior of sums and maxima of stationary discrete-valued processes. The asymptotic behavior is a cross between a central limit theorem and asymptotic bounds for the distribution of the maxima. Some applications and simulations are also included.

Sums and maxima of discrete stationary processes

1993 ◽  
Vol 30 (4) ◽  
pp. 863-876 ◽  
Author(s):  
William P. McCormick ◽  
Jiayang Sun
Keyword(s):  
Asymptotic Behavior ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Stationary Processes ◽  
Limiting Behavior ◽  
Asymptotic Bounds

This paper considers the joint limiting behavior of sums and maxima of stationary discrete-valued processes. The asymptotic behavior is a cross between a central limit theorem and asymptotic bounds for the distribution of the maxima. Some applications and simulations are also included.

On Gordin's central limit theorem for stationary processes

1975 ◽  
Vol 12 (1) ◽  
pp. 176-179 ◽  
Author(s):  
G. K. Eagleson
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Stationary Processes ◽  
The Central Limit Theorem ◽  
Mixture Of Normals

The central limit theorem for ergodic stationary processes obtained by Gordin is shown to hold for general stationary processes. In this case, the limit law is a mixture of normals.

The Hawkes Process with Different Exciting Functions and its Asymptotic Behavior

2015 ◽  
Vol 52 (01) ◽  
pp. 37-54 ◽  
Author(s):  
Raúl Fierro ◽  
Víctor Leiva ◽  
Jesper Møller
Keyword(s):  
Asymptotic Behavior ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Poisson Process ◽  
Central Limit ◽  
Law Of Large Numbers ◽  
Hawkes Process ◽  
Homogeneous Poisson Process ◽  
Large Numbers ◽  
Main Shocks

The standard Hawkes process is constructed from a homogeneous Poisson process and uses the same exciting function for different generations of offspring. We propose an extension of this process by considering different exciting functions. This consideration may be important in a number of fields; e.g. in seismology, where main shocks produce aftershocks with possibly different intensities. The main results are devoted to the asymptotic behavior of this extension of the Hawkes process. Indeed, a law of large numbers and a central limit theorem are stated. These results allow us to analyze the asymptotic behavior of the process when unpredictable marks are considered.

On Gordin's central limit theorem for stationary processes

1975 ◽  
Vol 12 (01) ◽  
pp. 176-179 ◽  
Author(s):  
G. K. Eagleson
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Stationary Processes ◽  
The Central Limit Theorem ◽  
Mixture Of Normals

The central limit theorem for ergodic stationary processes obtained by Gordin is shown to hold for general stationary processes. In this case, the limit law is a mixture of normals.

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