scholarly journals On the central limit theorem for the sum of a random number of independent random variables

1963 ◽  
Vol 1 (4) ◽  
pp. 389-393 ◽  
Author(s):  
J. R. Blum ◽  
D. L. Hanson ◽  
J. I. Rosenblatt
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Number ◽  
Random Variables ◽  
Independent Random Variables ◽  
The Central Limit Theorem

scholarly journals On Feller's criterion for the law of the iterated logarithm

1994 ◽  
Vol 17 (2) ◽  
pp. 323-340 ◽  
Author(s):  
Deli Li ◽  
M. Bhaskara Rao ◽  
Xiangchen Wang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Uniform Estimate ◽  
Random Variables ◽  
Independent Random Variables ◽  
Partial Sums ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
The Law

Combining Feller's criterion with a non-uniform estimate result in the context of the Central Limit Theorem for partial sums of independent random variables, we obtain several results on the Law of the Iterated Logarithm. Two of these results refine corresponding results of Wittmann (1985) and Egorov (1971). In addition, these results are compared with the corresponding results of Teicher (1974), Tomkins (1983) and Tomkins (1990)

scholarly journals On operator-valued monotone independence

2014 ◽  
Vol 215 ◽  
pp. 151-167 ◽  
Author(s):  
Takahiro Hasebe ◽  
Hayato Saigo
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Generating Functions ◽  
Conditional Expectation ◽  
Random Variables ◽  
Independent Random Variables ◽  
The Central Limit Theorem ◽  
Noncommutative Version ◽  
The Moment

AbstractWe investigate operator-valued monotone independence, a noncommutative version of independence for conditional expectation. First we introduce operator-valued monotone cumulants to clarify the whole theory and show the moment-cumulant formula. As an application, one can obtain an easy proof of the central limit theorem for the operator-valued case. Moreover, we prove a generalization of Muraki’s formula for the sum of independent random variables and a relation between generating functions of moments and cumulants.

Sign in / Sign up

Export Citation Format

Share Document