scholarly journals On the use of fractional calculus for the probabilistic characterization of random variables

2009 ◽  
Vol 24 (3) ◽  
pp. 321-330 ◽  
Author(s):  
Giulio Cottone ◽  
Mario Di Paola
Keyword(s):  
Fractional Calculus ◽  
Random Variables ◽  
Probabilistic Characterization

scholarly journals HEYDE’S CHARACTERIZATION THEOREM FOR DISCRETE ABELIAN GROUPS

2010 ◽  
Vol 88 (1) ◽  
pp. 93-102 ◽  
Author(s):  
MARGARYTA MYRONYUK
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Real Line ◽  
Linear Form ◽  
Conditional Distribution ◽  
Random Variables ◽  
Characterization Theorem ◽  
Gaussian Distributions ◽  
Discrete Abelian Group

AbstractLet X be a countable discrete abelian group with automorphism group Aut(X). Let ξ1 and ξ2 be independent X-valued random variables with distributions μ1 and μ2, respectively. Suppose that α1,α2,β1,β2∈Aut(X) and β1α−11±β2α−12∈Aut(X). Assuming that the conditional distribution of the linear form L2 given L1 is symmetric, where L2=β1ξ1+β2ξ2 and L1=α1ξ1+α2ξ2, we describe all possibilities for the μj. This is a group-theoretic analogue of Heyde’s characterization of Gaussian distributions on the real line.

Probabilistic characterization of subsurface stratigraphic configuration with modified random field approach

2021 ◽  
pp. 106138
Author(s):  
Chao Zhao ◽  
Wenping Gong ◽  
Tianzheng Li ◽  
C. Hsein Juang ◽  
Huiming Tang ◽  
...  
Keyword(s):  
Random Field ◽  
Field Approach ◽  
Probabilistic Characterization
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