A multivariate Faa di Bruno formula with applications

Transactions of the American Mathematical Society

Volumn 348, Issue 2, 1996, Pages 503-520

  Constantine, G M ^a   Savits, T H ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Multivariate Stirling numbers; Partial derivatives; Set partitions; Stochastic processes

Indexed keywords

EID: 21344454432     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-96-01501-2     Document Type: Article

References (12)

1. Chen, C. S. and Savits, T. H. (1993). Some remarks on compound nonhomogenous Poisson processes. Statistics and Probability Letters, 17, 179-187.MR 94b:60056
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. 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 independante Darstellung der höheren differentialquotienten.Mathematische Annalen, 4, 85-87.
6. Hsu, L. C. (1993). Finding some strange identities via Faa di Bruno's formula.Math. Research and Exposition, 13, 159-165.MR 94f:05007
7. Lacroix, S. F. (1810). Traité du calcul integral. Tome Premier, Paris.
8. Lovász, L. (1979). Combinatorial problems and exercises. North-Holland, Amsterdam.MR 80m:05001
9. Lukacs, E. (1955). Applications of Faa di Bruno's formula in mathematical statistics. Am.Math.Monthly, 62, 340-348.MR 16:1037g
10. McCullagh, P. (1987). Tensor Methods in Statistics. Chapman and Hall, New York.MR 88k:62004
11. Most, R. (1871). Ueber die hoheren differentialquotienten.Mathematische Annalen, 4, 499-504.
12. Parzen, E. (1962). Stochastic Processes. Holden-Day, San Francisco.MR 25:2628