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Abstract: : Classic works of Karlin-McGregor and Jones-Magnus have established a general correspondence between continuous-time birth-and-death processes and continued fractions of the Stieltjes-Jacobi type together with their associated orthogonal polynomials. This fundamental correspondence is revisited here in the light of the basic relation between weighted lattice paths and continued fractions otherwise known from combinatorial theory. Given that trajectories of the embedded Markov chain of a... (Update)
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BibTeX entry: (Update)
@misc{ flajolet-formal,
author = "Philippe Flajolet and Fabrice Guillemin",
title = "The Formal Theory of Birth-and-Death Processes, Lattice Path Combinatorics,
and Continued Fractions",
url = "citeseer.comp.nus.edu.sg/12513.html" }
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222 Applied probability and queues (context) - Asmussen - 1987
172 Applied and Computational Complex Analysis (context) - Henrici - 1977
156 An Introduction to Orthogonal Polynomials (context) - Chihara - 1978
154 Combinatorial Enumeration (context) - Goulden, Jackson - 1983
148 A First Course in Stochastic Processes (context) - Karlin, Taylor - 1975
143 Higher Transcendental Functions (context) - Erd'elyi - 1953
62 Special functions and their applications (context) - Lebedev - 1965
61 Combinatorial aspects of continued fractions (context) - Flajolet - 1980
48 Chapman and Hall (context) - Godsil - 1993
33 Numerical inversion of Laplace transforms of probability dis.. (context) - Abate, Whitt - 1995
30 Cambridge University Press (context) - Norris - 1997
27 Continued Fractions: Analytic Theory and Applications (context) - Jones, Thron - 1990
16 The classification of birth and death processes (context) - Karlin, Gregor - 1957
11 Sequence of operations analysis for dynamic data structures (context) - Flajolet, Fran et al. - 1980
10 Bessel functions and a divergent series (context) - Flajolet, Schott et al. - 1990
8 On congruences and continued fractions for some classical co.. (context) - Flajolet - 1982
8 The differential equation of birth and death processes (context) - Karlin, Gregor - 1957
6 The analysis of simple list structure (context) - Flajolet, Puech et al. - 1986
5 Linear birth and death models and associated Laguerre and Me.. (context) - Ismail, Letessier et al. - 1988
5 Memoirs of the American Mathematical Society (context) - Askey, Ismail et al. - 1984
4 Computing Laplace transforms for numerical inversion via con.. - Abate, Whitt - 1995
4 Continued fraction analysis of the duration of an excursion .. (context) - Guillemin, Pinchon - 1998
4 Birth and death processes and orthogonal polynomials (context) - Ismail, Letessier et al. - 1990
3 Applications of Stieltjes theory for S-fractions to birth an.. (context) - Bordes, Roehner - 1983
2 Application of Stieltjes fractions to birth-death processes (context) - Jones, Magnus - 1977
2 Random Motion and Analytic Continued Fractions (context) - Good - 1958
1 Linear growth birth and death processes (context) - Karlin, Gregor - 1958
1 Laplace transforms of density probability density functions .. (context) - Abate, Whitt - 1998
1 transience revisited (context) - Preater - 1998
1 Excursions of birth an death processes (context) - Guillemin, Pinchon - 1999
1 a random variable associated with excursion in an M=M=1 syst.. (context) - Guillemin, Pinchon - 1999
1 Path Generating functions and continued fractions (context) - Goulden, Jackson - 1986
1 the area swept under the occupation process of an M=M=1 queu.. (context) - Guillemin, Pinchon - 1998
1 The Single Sever Queue (context) - Cohen - 1982
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