scholarly journals Principal Functions for Bi-free Central Limit Distributions

2016 ◽  
Vol 85 (1) ◽  
pp. 91-108
Author(s):  
Kenneth J. Dykema ◽  
Wonhee Na
Keyword(s):  
Central Limit ◽  
Limit Distributions

On the asymptotic distribution of multivariate renewal processes

1984 ◽  
Vol 21 (3) ◽  
pp. 639-645 ◽  
Author(s):  
Ştefan P. Niculescu
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Rate Of Convergence ◽  
Asymptotic Distribution ◽  
Central Limit ◽  
Renewal Theory ◽  
Renewal Processes ◽  
Limit Distributions ◽  
Multidimensional Central Limit Theorem

Using a result of Bikjalis (1971) concerning the rate of convergence in the multidimensional central limit theorem we obtain informations about some limit distributions in multivariate renewal theory.

On the asymptotic distribution of multivariate renewal processes

1984 ◽  
Vol 21 (03) ◽  
pp. 639-645 ◽  
Author(s):  
Ştefan P. Niculescu
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Rate Of Convergence ◽  
Asymptotic Distribution ◽  
Central Limit ◽  
Renewal Theory ◽  
Renewal Processes ◽  
Limit Distributions ◽  
Multidimensional Central Limit Theorem

Using a result of Bikjalis (1971) concerning the rate of convergence in the multidimensional central limit theorem we obtain informations about some limit distributions in multivariate renewal theory.

scholarly journals CONDITIONALLY MONOTONE INDEPENDENCE I: INDEPENDENCE, ADDITIVE CONVOLUTIONS AND RELATED CONVOLUTIONS

2011 ◽  
Vol 14 (03) ◽  
pp. 465-516 ◽  
Author(s):  
TAKAHIRO HASEBE
Keyword(s):  
Probability Theory ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Infinite Divisibility ◽  
Noncommutative Probability ◽  
Limit Distributions ◽  
Boolean Products ◽  
Probability Spaces ◽  
Orthogonal Product

We define a product of algebraic probability spaces equipped with two states. This product is called a conditionally monotone product. This product is a new example of independence in noncommutative probability theory and unifies the monotone and Boolean products, and moreover, the orthogonal product. Then we define the associated cumulants and calculate the limit distributions in central limit theorem and Poisson's law of small numbers. We also prove a combinatorial moment-cumulant formula using monotone partitions. We investigate some other topics such as infinite divisibility for the additive convolution and deformations of the monotone convolution. We define cumulants for a general convolution to analyze the deformed convolutions.

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