## A Multivariate Faa di Bruno Formula with Applications

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- by G. M. Constantine and T. H. Savits PDF
- Trans. Amer. Math. Soc.
**348**(1996), 503-520 Request permission

## 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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## 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
- 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