A spectral weight matrix for a discrete version of Walsh’s spider

Operator Theory: Advances and Applications

Volumn 202, Issue , 2010, Pages 253-264

  Grünbaum, F Alberto ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Karlin McGregor representation; Matrix valued orthogonal polynomials

Indexed keywords

EID: 84975760203     PISSN: 02550156     EISSN: 22964878     Source Type: Book Series    
DOI: 10.1007/978-3-0346-0158-0_12     Document Type: Conference Paper

References (15)

1. Basu, S., and Bose, N.K., Matrix Stieltjes series and network models, SIAM J. Matrix Anal. Applic. 14, No. 2 (1983), 209-222.
2. Dette, H., Reuther, B., Studden, W. and Zygmunt, M., Matrix measures and random walks with a block tridiagonal transition matrix, SIAM J. Matrix Anal. Applic. 29, No. 1 (2006), 117-142.
3. van Doorn, E., On associated polynomials and decay rates for birth-death processes, J. Math. Anal. Appl. 278, No. 2 (2003), 500-511.
4. Evans, S. and Sowers, R., Pinching and twisting Markov processes, Ann. Probab. 31(2003), no. 1, pp. 486-527.
5. Grünbaum, F.A., Random walks and orthogonal polynomials: some challenges, in Probability, Geometry and Integrable systems, Mark Pinsky and Bjorn Birnir editors, MSRI publication vol 55, 2007, pp. 241-260, see also arXiv math PR/0703375.
6. Grünbaum, F.A., QBD processes and matrix-valued orthogonal polynomials: some new explicit examples, Dagstuhl Seminar Proceedings 07461, Numerical Methods in structured Markov Chains, 2007, D. Bini editor.
7. Grünbaum, F.A. and de la Iglesia, M.D., Matrix-valued orthogonal polynomials arising from group representation theory and a family of quasi-birth-and-death processes, Siam J. Matrix Anal. Appl. Vol. 30, 2, pp. 741-763, 2008.
8. Ismail, M.E.H., Letessier, J., Masson, D., and Valent, G., Birth and death processes and orthogonal polynomials, in Orthogonal Polynomials, P. Nevai (editor), Kluwer Acad. Publishers (1990), 229-255.
9. Karlin, S., and McGregor, J., Random walks, Illinois J. Math. 3 (1959), 66-81
10. Krein, M.G., Fundamental aspects of the representation theory of hermitian operators with deficiency index (m, m), AMS Translations, Series 2, vol. 97, Prov- idence, Rhode Island (1971), 75-143.
11. Krein, M.G., Infinite J -matrices and a matrix moment problem, Dokl. Akad. Nauk SSSR 69, nr. 2 (1949), 125-128.
12. Latouche, G., and Ramaswami, V., Introduction to Matrix Analytic Methods in Stochastic Modeling, ASA-SIAM Series on Statistics and Applied Probability, 1999.
13. Latouche, G., Pearce, C.E.M., and Taylor, P.G., Invariant measures for quasi-birth-and-death processes, Comm. Statist. Stochastic Models, 14 (1998), 443-460.
14. Neuts, M.F., Structured Stochastic Matrices of M/G/1 Type and Their Applications, Marcel Dekker, NY, 1989.
15. Walsh, J.B., A diffusion with discontinuous local time, in Temps Locaux, Astérisque, vol. 52-53 Soc. Math. de France, Paris, 1978.