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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A Multivariate Faa di Bruno Formula
with Applications


Authors: G. M. Constantine and T. H. Savits
Journal: Trans. Amer. Math. Soc. 348 (1996), 503-520
MSC (1991): Primary 05A17, 05A19; Secondary 26B05, 60G20
MathSciNet review: 1325915
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Abstract: A multivariate Faa di Bruno formula for computing arbitrary partial derivatives of a function composition is presented. It is shown, by way of a general identity, how such derivatives can also be expressed in the form of an infinite series. Applications to stochastic processes and multivariate cumulants are then delineated.


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Additional Information

G. M. Constantine
Affiliation: Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: gmc@vms.cis.pitt.edu

T. H. Savits
Affiliation: Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: ths@stat.pitt.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01501-2
PII: S 0002-9947(96)01501-2
Keywords: Partial derivatives, set partitions, multivariate Stirling numbers, stochastic processes
Received by editor(s): January 20, 1994
Additional Notes: The first author was funded under a Fulbright grant; the second author was supported by NSF DMS-9203444 and NSA MDA 904-95-H1011
Article copyright: © Copyright 1996 American Mathematical Society