Abstract
We investigate operator-valued monotone independence, a noncommutative version of independence for conditional expectation. First we introduce operator-valued monotone cumulants to clarify the whole theory and show the moment-cumulant formula. As an application, one can obtain an easy proof of the central limit theorem for the operator-valued case. Moreover, we prove a generalization of Muraki’s formula for the sum of independent random variables and a relation between generating functions of moments and cumulants.
Citation
Takahiro Hasebe. Hayato Saigo. "On operator-valued monotone independence." Nagoya Math. J. 215 151 - 167, September 2014. https://doi.org/10.1215/00277630-2741151
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