Independence and Product Systems

Details Independence and Product Systems Independence and Product Systems

2003-08-26

arxiv.org/abs/math/0308245v1

In S. Albeverio, Z.-M. Ma, and M. R\"ockner, editors, Recent developments in stochastic analysis and related topics. World Sci

Mathematics

Operator Algebras

To appear in Proceedings of the ``First Sino-German Meeting on Stochastic Analysis'', Beijing, 2002

Scientific paper

Starting from elementary considerations about independence and Markov
processes in classical probability we arrive at the new concept of conditional
monotone independence (or operator-valued monotone independence). With the help
of product systems of Hilbert modules we show that monotone conditional
independence arises naturally in dilation theory.

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