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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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A Multivariate Faa di Bruno Formula with Applications
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by G. M. Constantine and T. H. Savits
Trans. Amer. Math. Soc. 348 (1996), 503-520
DOI: https://doi.org/10.1090/S0002-9947-96-01501-2
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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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Bibliographic 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
  • 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
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 503-520
  • MSC (1991): Primary 05A17, 05A19; Secondary 26B05, 60G20
  • DOI: https://doi.org/10.1090/S0002-9947-96-01501-2
  • MathSciNet review: 1325915