Results 1 
1 of
1
What is stochastic independence
"... The notion of a tensor product with projections or with inclusions is defined. It is shown that the definition of stochastic independence relies on such a structure and that independence can be defined in an arbitrary category with a tensor product with inclusions or projections. In this context, th ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
The notion of a tensor product with projections or with inclusions is defined. It is shown that the definition of stochastic independence relies on such a structure and that independence can be defined in an arbitrary category with a tensor product with inclusions or projections. In this context, the classifications of quantum stochastic independence by Muraki, Ben Ghorbal, and Schürmann become classifications of the tensor products with inclusions for the categories of algebraic probability spaces and nonunital algebraic probability spaces. The notion of a reduction of one independence to another is also introduced. As examples the reductions of Fermi independence and boolean, monotone, and antimonotone independence to tensor independence are presented. 1