Infinitely Divisible Probabilities And Central Limit Theorem Associated With The Bessel Operator

2001 ◽  
pp. 185-208
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Bessel Operator ◽  
Infinitely Divisible

scholarly journals A martingale central limit theorem without negligibility conditions

1978 ◽  
Vol 18 (1) ◽  
pp. 13-19 ◽  
Author(s):  
Robert J. Adler
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Sufficient Conditions ◽  
Infinitely Divisible ◽  
Martingale Central Limit Theorem ◽  
Triangular Arrays ◽  
Infinitely Divisible Laws ◽  
Martingale Case

We obtain sufficient conditions for the convergence of martingale triangular arrays to infinitely divisible laws with finite variances, without making the usual assumptions of uniform asymptotic negligibility. Our results generalise known results for both the martingale case under a negligibility assumption and the classical (independence) case without such assumptions.

scholarly journals Central limit theorem for mean and variogram estimators in Lévy–based models

2019 ◽  
Vol 56 (01) ◽  
pp. 209-222
Author(s):  
Anders Rønn-Nielsen ◽  
Eva B. Vedel Jensen
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Field ◽  
Central Limit ◽  
Kernel Function ◽  
Limit Theorems ◽  
Regularity Conditions ◽  
Infinitely Divisible ◽  
The Mean ◽  
The Moment

AbstractWe consider an infinitely divisible random field in ℝd given as an integral of a kernel function with respect to a Lévy basis. Under mild regularity conditions, we derive central limit theorems for the moment estimators of the mean and the variogram of the field.

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