A Multivariate Faa di Bruno Formula with Applications

1996/01/01 by G. Constantine, Gregory M. Constantine, T. Savits +1 · 444 citations
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Cumulant #Identity (music) #Mathematical functions and polynomials #Mathematics #Multivariate analysis #Multivariate statistics #Polynomial and algebraic computation #Pure mathematics #Scientific Research and Discoveries #Series (stratigraphy) #Statistics

paper · pdf · doi:10.1090/s0002-9947-96-01501-2

published in Transactions of the American Mathematical Society 348(2), 503-520 (American Mathematical Society)

openalex publication_date 1996/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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