Noncommutative Probability and Multiplicative Cascades

2021 ◽  
Vol 36 (2) ◽  
Author(s):  
Ian W. McKeague
Keyword(s):  
Noncommutative Probability ◽  
Multiplicative Cascades

scholarly journals Diffusions of multiplicative cascades

2014 ◽  
Vol 124 (2) ◽  
pp. 1141-1169
Author(s):  
Tom Alberts ◽  
Ben Rifkind
Keyword(s):  
Multiplicative Cascades

THE FIVE INDEPENDENCES AS NATURAL PRODUCTS

2003 ◽  
Vol 06 (03) ◽  
pp. 337-371 ◽  
Author(s):  
NAOFUMI MURAKI
Keyword(s):  
Probability Theory ◽  
Natural Products ◽  
Tensor Product ◽  
Natural Product ◽  
Free Product ◽  
Noncommutative Probability ◽  
Stochastic Independence ◽  
Boolean Product ◽  
Probability Spaces ◽  
Noncommutative Probability Theory

Let [Formula: see text] be the class of all algebraic probability spaces. A "natural product" is, by definition, a map [Formula: see text] which is required to satisfy all the canonical axioms of Ben Ghorbal and Schürmann for "universal product" except for the commutativity axiom. We show that there exist only five natural products, namely tensor product, free product, Boolean product, monotone product and anti-monotone product. This means that, in a sense, there exist only five universal notions of stochastic independence in noncommutative probability theory.

Multiplicative cascades and seismicity in natural time

2009 ◽  
Vol 80 (2) ◽  
Author(s):  
N. V. Sarlis ◽  
E. S. Skordas ◽  
P. A. Varotsos
Keyword(s):  
Multiplicative Cascades ◽  
Natural Time

scholarly journals Relations between cumulants in noncommutative probability

2015 ◽  
Vol 282 ◽  
pp. 56-92 ◽  
Author(s):  
Octavio Arizmendi ◽  
Takahiro Hasebe ◽  
Franz Lehner ◽  
Carlos Vargas
Keyword(s):  
Noncommutative Probability
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