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A Multivariate Faa di Bruno Formula with Applications
Author(s):
G.
M.
Constantine;
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.
References:
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- 2.
- Constantine, G. M. (1987). Combinatorial Theory and Statistical Design. Wiley, New York. MR 88k:05001
- 3.
- Constantine, G. M. and Savits, T. H. (1994). A stochastic process interpretation of partition identities. SIAM J. Discrete Mathematics, 2, 194-202. MR 95d:05010
- 4.
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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:
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
Copyright of article:
Copyright
1996,
American Mathematical Society
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