Cumulant–Cumulant Relations in Free Probability Theory from Magnus’ Expansion
نویسندگان
چکیده
Relations between moments and cumulants play a central role in both classical non-commutative probability theory. The latter allows for several distinct families of corresponding to different types independences: free, Boolean monotone. among those have been studied recently. In this work we focus on the problem expressing with closed formula multivariate monotone terms free cumulants. process introduce various constructions statistics non-crossing partitions. Our approach is based pre-Lie algebra structure cumulant functionals. are described Magnus expansion combined results continuous Baker-Campbell-Hausdorff due A. Murua.
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2021
ISSN: ['1615-3383', '1615-3375']
DOI: https://doi.org/10.1007/s10208-021-09512-0