Δ-Cumulants in terms of moments
2018 ◽
Vol 21
(02)
◽
pp. 1850012
Keyword(s):
The [Formula: see text]-convolution of real probability measures, introduced by Bożejko, generalizes both free and Boolean convolutions. It is linearized by the [Formula: see text]-cumulants, and Yoshida gave a combinatorial formula for moments in terms of [Formula: see text]-cumulants, that implicitly defines the latter. It relies on the definition of an appropriate weight on noncrossing partitions. We give here two different expressions for the [Formula: see text]-cumulants: the first one is a simple variant of Lagrange inversion formula, and the second one is a combinatorial inversion of Yoshida’s formula involving Schröder trees.
Keyword(s):
1964 ◽
Vol 17
(2)
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pp. 137-146
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2001 ◽
Vol 45
(1)
◽
pp. 164-172
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1987 ◽
Vol 45
(2)
◽
pp. 178-195
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Keyword(s):
1980 ◽
Vol 257
(2)
◽
pp. 455-455
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Keyword(s):