메뉴 건너뛰기




Volumn 31, Issue 5, 2010, Pages 2239-2260

Quasi-birth-and-death processes and matrix-valued orthogonal polynomials

Author keywords

Block tridiagonal matrix; Karlin McGregor representation; Markov chains; Matrix valued orthogonal polynomials; Quasi birth and death process

Indexed keywords

KARLIN-MCGREGOR REPRESENTATION; MARKOV CHAIN; MATRIX; QUASI-BIRTH-AND-DEATH PROCESS; TRIDIAGONAL MATRICES;

EID: 79251494117     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/080742816     Document Type: Article
Times cited : (15)

References (35)
  • 1
    • 0001324627 scopus 로고
    • Asymptotic fringe distributions for general families of random trees
    • D. Aldous, Asymptotic fringe distributions for general families of random trees, Ann. Appl. Probab., 1 (1991), pp. 228-266.
    • (1991) Ann. Appl. Probab. , vol.1 , pp. 228-266
    • Aldous, D.1
  • 3
    • 0000578402 scopus 로고
    • The scattering problem for a discrete Sturm-Liouville operator
    • A. Aptekarev and E. Nikishin, The scattering problem for a discrete Sturm-Liouville operator, Mat. Sb., 121 (1983), pp. 327-358.
    • (1983) Mat. Sb. , vol.121 , pp. 327-358
    • Aptekarev, A.1    Nikishin, E.2
  • 5
    • 0003316646 scopus 로고
    • Expansions in eigenfunctions of selfadjoint operators
    • AMS, Providence, RI
    • J. Berezanskii, Expansions in Eigenfunctions of Selfadjoint Operators, Transl. Math. Monogr. 17, AMS, Providence, RI, 1968.
    • (1968) Transl. Math. Monogr. , vol.17
    • Berezanskii, J.1
  • 6
    • 84959949711 scopus 로고
    • Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes
    • L. W. Bright and P. G. Taylor, Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes, Comm. Statist. Stochastic Models, 11 (1995), pp. 497-514.
    • (1995) Comm. Statist. Stochastic Models , vol.11 , pp. 497-514
    • Bright, L.W.1    Taylor, P.G.2
  • 7
    • 59349095511 scopus 로고    scopus 로고
    • The analytic theory of matrix orthogonal polynomials
    • D. Damanik, A. Pushnitski, and B. Simon, The analytic theory of matrix orthogonal polynomials, Surv. Approx. Theory, 4 (2008), pp. 1-85.
    • (2008) Surv. Approx. Theory , vol.4 , pp. 1-85
    • Damanik, D.1    Pushnitski, A.2    Simon, B.3
  • 8
    • 39449110777 scopus 로고    scopus 로고
    • Matrix measures and random walks with a block tridiagonal transition matrix
    • H. Dette, B. Reuther, W. J. Studden, and M. Zygmunt, Matrix measures and random walks with a block tridiagonal transition matrix, SIAM J. Matrix Anal. Appl., 29 (2006), pp. 117-142.
    • (2006) SIAM J. Matrix Anal. Appl. , vol.29 , pp. 117-142
    • Dette, H.1    Reuther, B.2    Studden, W.J.3    Zygmunt, M.4
  • 10
    • 38249001187 scopus 로고
    • A generalization of Favard's theorem for polynomials satisfying a recurrence relation
    • A. J. Duran, A generalization of Favard's theorem for polynomials satisfying a recurrence relation, J. Approx. Theory, 74 (1993), pp. 83-109.
    • (1993) J. Approx. Theory , vol.74 , pp. 83-109
    • Duran, A.J.1
  • 11
    • 0000169130 scopus 로고    scopus 로고
    • Ratio asymptotics for orthogonal matrix polynomials
    • A. J. Duran, Ratio asymptotics for orthogonal matrix polynomials, J. Approx. Theory, 100 (1999), pp. 304-344.
    • (1999) J. Approx. Theory , vol.100 , pp. 304-344
    • Duran, A.J.1
  • 12
    • 0029692953 scopus 로고    scopus 로고
    • Orthogonal matrix polynomials: Zeros and Blumenthal's theorem
    • A. J. Duran and P. Lopez-Rodriguez, Orthogonal matrix polynomials: Zeros and Blumenthal's theorem, J. Approx. Theory, 84 (1996), pp. 96-118.
    • (1996) J. Approx. Theory , vol.84 , pp. 96-118
    • Duran, A.J.1    Lopez-Rodriguez, P.2
  • 13
    • 0004117869 scopus 로고    scopus 로고
    • Essentials of stochastic processes
    • Springer-Verlag, New York
    • R. Durrett, Essentials of Stochastic Processes, Springer Texts Statist., Springer-Verlag, New York, 1999.
    • (1999) Springer Texts Statist.
    • Durrett, R.1
  • 15
    • 0034266828 scopus 로고    scopus 로고
    • The formal theory of birth-and-death processes, lattice path combinatorics and continued fractions
    • P. Flajolet and F. Guillemin, The formal theory of birth-and-death processes, lattice path combinatorics and continued fractions, Adv. in Appl. Probab., 32 (2000), pp.750-778.
    • (2000) Adv. in Appl. Probab. , vol.32 , pp. 750-778
    • Flajolet, P.1    Guillemin, F.2
  • 17
    • 59349114321 scopus 로고    scopus 로고
    • Random walks and orthogonal polynomials: Some challenges
    • Cambridge University Press, Cambridge, UK
    • F. A. Gr̈unbaum, Random walks and orthogonal polynomials: Some challenges, in Geometry and Integrable Systems, Math. Sci. Res. Inst. Publ. 55, Cambridge University Press, Cambridge, UK, pp. 241-260.
    • Geometry and Integrable Systems, Math. Sci. Res. Inst. Publ. , vol.55 , pp. 241-260
    • Gr̈unbaum, F.A.1
  • 18
    • 72449186799 scopus 로고    scopus 로고
    • QBD processes and matrix valued orthogonal polynomials: Some new explicit examples
    • Schloss Dagstuhl, Dagstuhl, Germany
    • F. A. Gr̈unbaum, QBD processes and matrix valued orthogonal polynomials: Some new explicit examples, in Numerical Methods for Structured Markov Chains, Schloss Dagstuhl, Dagstuhl, Germany, 2007.
    • (2007) Numerical Methods for Structured Markov Chains
    • Gr̈unbaum, F.A.1
  • 19
    • 59349119754 scopus 로고    scopus 로고
    • Matrix valued orthogonal polynomials arising from group representation theory and a family of quasi-birth-and-death processes
    • F. A. Gr̈unbaum and M. D. de la Iglesia, Matrix valued orthogonal polynomials arising from group representation theory and a family of quasi-birth-and-death processes, SIAM J. Matrix Anal. Appl., 30 (2008), pp. 741-761.
    • (2008) SIAM J. Matrix Anal. Appl. , vol.30 , pp. 741-761
    • Gr̈unbaum, F.A.1    De La Iglesia, M.D.2
  • 20
    • 0033236710 scopus 로고    scopus 로고
    • Excursions of birth and death processes, orthogonal polynomials, and continued fractions
    • F. Guillemin and D. Pinchon, Excursions of birth and death processes, orthogonal polynomials, and continued fractions, J. Appl. Probab., 36 (1999), pp. 752-770.
    • (1999) J. Appl. Probab. , vol.36 , pp. 752-770
    • Guillemin, F.1    Pinchon, D.2
  • 21
    • 23744473466 scopus 로고    scopus 로고
    • Pathological birth-and-death processes and the spectral theory of strings
    • I. S. Kac, Pathological birth-and-death processes and the spectral theory of strings, Funct. Anal. Appl., 39 (2005), pp. 144-147.
    • (2005) Funct. Anal. Appl. , vol.39 , pp. 144-147
    • Kac, I.S.1
  • 22
    • 84968465028 scopus 로고
    • The classification of birth and death processes
    • S. Karlin and J. McGregor, The classification of birth and death processes, Trans. Amer. Math. Soc., 86 (1957), pp. 366-400.
    • (1957) Trans. Amer. Math. Soc. , vol.86 , pp. 366-400
    • Karlin, S.1    McGregor, J.2
  • 24
    • 0002344242 scopus 로고
    • Linear growth models with many types and multidimensional Hahn polynomials
    • R. Askey, ed., Academic Press, New York
    • S. Karlin and J. McGregor, Linear growth models with many types and multidimensional Hahn polynomials, in Theory and Application of Special Functions, R. Askey, ed., Academic Press, New York, 1975, pp. 261-288.
    • (1975) Theory and Application of Special Functions , pp. 261-288
    • Karlin, S.1    McGregor, J.2
  • 25
    • 34047273475 scopus 로고
    • A multi-dimensional linear growth birth and death process
    • P. R. Milch, A multi-dimensional linear growth birth and death process, Ann. Math. Statist., 39 (1968), pp. 727-754.
    • (1968) Ann. Math. Statist. , vol.39 , pp. 727-754
    • Milch, P.R.1
  • 26
    • 0004239351 scopus 로고
    • Discrete-parameter martingales
    • Library 10, North-Holland, Amsterdam
    • J. Neveu, Discrete-Parameter Martingales, North-Holland Math. Library 10, North-Holland, Amsterdam, 1975.
    • (1975) North-Holland Math.
    • Neveu, J.1
  • 27
    • 84941455741 scopus 로고
    • Über potenzreihen die im Innern des einheitskreises beschränkt sind, I
    • (in German)
    • I. Schur, Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind, I, J. Reine Angew. Math., 147 (1917), pp. 205-232 (in German);
    • (1917) J. Reine Angew. Math. , Issue.147 , pp. 205-232
    • Schur, I.1
  • 28
    • 79251481939 scopus 로고
    • Birkhäuser, Basel, (in English)
    • I. Gohberg, ed., Oper. Theory Adv. Appl. 18, Birkhäuser, Basel, 1986 (in English).
    • (1986) Oper. Theory Adv. Appl. , vol.18
    • Gohberg, I.1
  • 29
    • 84941610524 scopus 로고
    • Über potenzreihen, die im Innern des einheitskreises beschränkt sind, II
    • (in German)
    • I. Schur, Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind, II, J. Reine Angew. Math. 148 (1918), pp. 122-145 (in German);
    • (1918) J. Reine Angew. Math. , vol.148 , pp. 122-145
    • Schur, I.1
  • 30
    • 79251512400 scopus 로고
    • Birkhäuser, Basel, (in English)
    • I. Gohberg, ed., Oper. Theory Adv. Appl. 18, Birkhäuser, Basel, 1986 (in English).
    • (1986) Oper. Theory Adv. Appl. , vol.18
    • Gohberg, I.1
  • 31
    • 0029712604 scopus 로고    scopus 로고
    • Orthogonal matrix polynomials and applications
    • A. Sinap and W. Van Assche, Orthogonal matrix polynomials and applications, J. Comput. Appl. Math., 66 (1996), pp. 27-52.
    • (1996) J. Comput. Appl. Math. , vol.66 , pp. 27-52
    • Sinap, A.1    Van Assche, W.2
  • 33
    • 0040093798 scopus 로고
    • Block Jacobi matrices and zeros of multivariate orthogonal polynomials
    • Y. Xu, Block Jacobi matrices and zeros of multivariate orthogonal polynomials, Trans. Amer. Math. Soc., 342 (1994), pp. 855-866.
    • (1994) Trans. Amer. Math. Soc. , vol.342 , pp. 855-866
    • Xu, Y.1
  • 34
    • 21344495829 scopus 로고
    • Recurrence formulas for orthogonal polynomials
    • Y. Xu, Recurrence formulas for orthogonal polynomials, Math. Comp., 62 (1994), pp. 687-702.
    • (1994) Math. Comp. , vol.62 , pp. 687-702
    • Xu, Y.1
  • 35
    • 84966248605 scopus 로고
    • Multivariate orthogonal polynomials and operator theory
    • Y. Xu, Multivariate orthogonal polynomials and operator theory, Trans. Amer. Math. Soc., 343 (1994), pp. 193-202.
    • (1994) Trans. Amer. Math. Soc. , vol.343 , pp. 193-202
    • Xu, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.