Generalizations to several variables of Lagrange's expansion, with applications to stochastic processes
Tóm tắt
A generalization to two independent variables of Lagrange's expansion of an inverse function was given by Stieltjes and proved rigorously by Poincaré. A new method of proof is given here that also provides a new and sometimes more convenient form of the generalization. The results are given for an arbitrary number of independent variables. Applications are pointed out to random branching processes, to queues with various types of customers, and to some enumeration problems.
Từ khóa
Tài liệu tham khảo
Jacobson, 1951, Lectures in abstract algebra, I
Behnke, 1933, Theorie der Funktionen mehrerer komplexen Veränderlichen
Whittle, 1955, Some distribution and moment formulae for the Markov chain, J. R. Statist. Soc., 17, 235
Kendall, 1951, The theory of queues, J. R. Statist. Soc., 13, 151
Sevasty'astov, 1951, The theory of branching random processes, Usp. Matem. Nauk, 6, 47
(25) Stieltjes T. J. An unpublished manuscript sent to C. Hermite.
Bochner, 1948, Several complex variables
Jeffreys, 1946, Methods of mathematical physics
Lagrange, Mém. Acad., 24, 25
1889, Collected mathematical papers, 9, 202
1889, Collected mathematical papers, 13, 26
1889, Collected mathematical papers, 11, 365
Good, 1951, Contribution to the discussion on D. G. Kendall's paper (16), J. R. Statist. Soc., 13, 182
Everett, 1948, Multiplicative systems in several variables, Los Alamos Scientific Laboratory, II, 23
Goursat, 1904, A course in mathematical analysis
Forsyth, 1914, Lectures introductory to the theory of functions of two complex variables
Mirsky, 1955, An introduction to linear algebra
1889, Collected mathematical papers, 3, 242
Whittaker, 1935, A course of modern analysis
Price, 1947, Review of a paper by C. Massonnet, Math. Rev., 8, 499
Whittaker, 1949, From Euclid to Eddington