Law of large numbers and central limit theorems through Jack generating functions

2021 ◽  
Vol 380 ◽  
pp. 107545
Author(s):  
Jiaoyang Huang
Keyword(s):  
Central Limit ◽  
Generating Functions ◽  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Central Limit Theorems ◽  
Large Numbers

scholarly journals Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps

2014 ◽  
Vol 51 (03) ◽  
pp. 699-712 ◽  
Author(s):  
Lingjiong Zhu
Keyword(s):  
Stochastic Process ◽  
Large Deviations ◽  
Central Limit ◽  
Limit Theorems ◽  
Point Processes ◽  
Law Of Large Numbers ◽  
Laplace Transforms ◽  
Hawkes Process ◽  
Large Numbers ◽  
Special Case

In this paper we propose a stochastic process, which is a Cox-Ingersoll-Ross process with Hawkes jumps. It can be seen as a generalization of the classical Cox-Ingersoll-Ross process and the classical Hawkes process with exponential exciting function. Our model is a special case of the affine point processes. We obtain Laplace transforms and limit theorems, including the law of large numbers, central limit theorems, and large deviations.

scholarly journals Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps

2014 ◽  
Vol 51 (3) ◽  
pp. 699-712 ◽  
Author(s):  
Lingjiong Zhu
Keyword(s):  
Stochastic Process ◽  
Large Deviations ◽  
Central Limit ◽  
Limit Theorems ◽  
Point Processes ◽  
Law Of Large Numbers ◽  
Laplace Transforms ◽  
Hawkes Process ◽  
Large Numbers ◽  
Special Case

In this paper we propose a stochastic process, which is a Cox-Ingersoll-Ross process with Hawkes jumps. It can be seen as a generalization of the classical Cox-Ingersoll-Ross process and the classical Hawkes process with exponential exciting function. Our model is a special case of the affine point processes. We obtain Laplace transforms and limit theorems, including the law of large numbers, central limit theorems, and large deviations.

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