A Multivariate Faa di Bruno Formula with Applications

1996/01/01 by G. Constantine, Gregory M. Constantine, T. Savits +1 · 31 citations
Computer Science · Mathematics · Physics and Astronomy · #Polynomial and algebraic computation #Mathematical functions and polynomials #Scientific Research and Discoveries

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

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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