A Multivariate Faa di Bruno Formula with Applications-Reference-Cited by-同舟云学术

A Multivariate Faa di Bruno Formula with Applications

Published:1996 Issue:2 Volume:348 Page:503-520
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Constantine G.,Savits T.

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1996-348-02/S0002-9947-96-01501-2/S0002-9947-96-01501-2.pdf

Reference12 articles.

1. Some remarks on compound nonhomogeneous Poisson processes;Chen, C. S.;Statist. Probab. Lett.,1993

2. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics;Constantine, Gregory M.,1987

3. A stochastic process interpretation of partition identities;Constantine, G. M.;SIAM J. Discrete Math.,1994

4. Faa di Bruno, C. F. (1855). Note sur une nouvelle formule du calcul differentiel. Quart. J. Math., 1, 359-360.

5. Hoppe, R. (1871). Ueber independente Darstellung der höheren differentialquotienten. Mathematische Annalen, 4, 85-87.

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