Free Access
Issue
ESAIM: PS
Volume 14, 2010
Page(s) 117 - 150
DOI https://doi.org/10.1051/ps:2008037
Published online 10 May 2010
  1. D. Aldous and P. Diaconis, Strong uniform times and finite random walks. Adv. Appl. Math. 8 (1987) 69–97. [CrossRef] [Google Scholar]
  2. D. Aldous and J. Fill, Reversible Markov chains and random walks on graphs. Monograph in preparation, available on the web site: http://www.stat.berkeley.edu/∼aldous/RWG/book.html (1994-2002). [Google Scholar]
  3. R.F. Botta, C.M. Harris and W.G. Marchal, Characterizations of generalized hyperexponential distribution functions. Commun. Statist. Stoch. Models 3 (1987) 115–148. [CrossRef] [Google Scholar]
  4. C. Commault and S. Mocanu, Phase-type distributions and representations: some results and open problems for system theory. Int. J. Control 76 (2003) 566–580. [CrossRef] [Google Scholar]
  5. P. Diaconis and J.A. Fill, Strong stationary times via a new form of duality. Ann. Probab. 18 (1990) 1483–1522. [CrossRef] [MathSciNet] [Google Scholar]
  6. P. Diaconis and L. Miclo, On times to quasi-stationarity for birth and death processes. J. Theoret. Probab. 22 (2009) 558–586. [CrossRef] [MathSciNet] [Google Scholar]
  7. P. Diaconis and L. Saloff-Coste, Separation cut-offs for birth and death chains. Ann. Appl. Probab. 16 (2006) 2098–2122. [CrossRef] [MathSciNet] [Google Scholar]
  8. J. Ding, E. Lubetzky and Y. Peres, Total variation cutoff in birth-and-death chains. Probab. Theory Relat. Fields 146 (2010) 61–85. [CrossRef] [Google Scholar]
  9. P.D. Egleston, T.D. Lenker and S.K. Narayan, The nonnegative inverse eigenvalue problem. Linear Algebra Appl. 379 (2004) 475–490. [CrossRef] [MathSciNet] [Google Scholar]
  10. J.A. Fill, Strong stationary duality for continuous-time Markov chains, Part I: Theory. J. Theoret. Probab. 5 (1992) 45–70. [CrossRef] [MathSciNet] [Google Scholar]
  11. J.A. Fill, The passage time distribution for a birth-and-death chain: Strong stationary duality gives a first stochastic proof. J. Theoret. Probab. 22 (2009) 543–557. [CrossRef] [MathSciNet] [Google Scholar]
  12. J.A. Fill, On hitting times and fastest strong stationary times for skip-free processes. J. Theoret. Probab. 22 (2009) 587–600. [CrossRef] [MathSciNet] [Google Scholar]
  13. Qi-Ming He and Hanqin Zhang, Spectral polynomial algorithms for computing bi-diagonal representations for phase type distributions and matrix-exponential distributions. Stoch. Models 22 (2006) 289–317. [CrossRef] [MathSciNet] [Google Scholar]
  14. Qi-Ming He and Hanqin Zhang, PH-invariant polytopes and Coxian representations of phase type distributions. Stoch. Models 22 (2006) 383–409. [CrossRef] [MathSciNet] [Google Scholar]
  15. S. Karlin and J. McGregor, Coincidence properties of birth and death processes. Pacific J. Math. 9 (1959) 1109–1140. [MathSciNet] [Google Scholar]
  16. T. Kato, Perturbation theory for linear operators. Classics in Mathematics. Springer-Verlag, Berlin (1995). Reprint of the 1980 edition. [Google Scholar]
  17. J. Keilson, Log-concavity and log-convexity in passage time densities of diffusion and birth-death processes. J. Appl. Probab. 8 (1971) 391–398. [CrossRef] [Google Scholar]
  18. J.T. Kent, Eigenvalue expansions for diffusion hitting times, Z. Wahrsch. Verw. Gebiete 52 (1980) 309–319. [Google Scholar]
  19. J.T. Kent, The spectral decomposition of a diffusion hitting time. Ann. Probab. 10 (1982) 207–219. [CrossRef] [MathSciNet] [Google Scholar]
  20. J.T. Kent, The appearance of a multivariate exponential distribution in sojourn times for birth-death and diffusion processes. In Probability, statistics and analysis. London Math. Soc. Lect. Note Ser. 79. Cambridge Univ. Press, Cambridge (1983) 161–179. [Google Scholar]
  21. C.A. Micchelli and R.A. Willoughby, On functions which preserve the class of Stieltjes matrices. Linear Algebra Appl. 23 (1979) 141–156. [CrossRef] [MathSciNet] [Google Scholar]
  22. M.F. Neuts, Matrix-geometric solutions in stochastic models, Johns Hopkins Series in the Mathematical Sciences: An algorithmic approach, Vol. 2. Johns Hopkins University Press, Baltimore, MD (1981). [Google Scholar]
  23. C.A. O'Cinneide, Characterization of phase-type distributions. Commun. Statist. Stoch. Models 6 (1990) 1–57. [CrossRef] [Google Scholar]
  24. C.A. O'Cinneide, Phase-type distributions and invariant polytopes. Adv. Appl. Probab. 23 (1991) 515–535. [CrossRef] [Google Scholar]
  25. C.A. O'Cinneide, Phase-type distributions: open problems and a few properties. Commun. Statist. Stoch. Models 15 (1999) 731–757. [CrossRef] [Google Scholar]

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