The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


  • Billiard, Sylvain; Tran, Viet Chi. A general stochastic model for sporophytic self-incompatibility. J. Math. Biol. 64 (2012), no. 1-2, 163--210. MR2864842
  • Brezis, Haïm. Analyse fonctionnelle. (French) [Functional analysis] Théorie et applications. [Theory and applications] Collection Mathématiques Appliquées pour la Maîtrise. [Collection of Applied Mathematics for the Master's Degree] Masson, Paris, 1983. xiv+234 pp. ISBN: 2-225-77198-7 MR0697382
  • Cattiaux, Patrick; Collet, Pierre; Lambert, Amaury; Martínez, Servet; Méléard, Sylvie; San Martín, Jaime. Quasi-stationary distributions and diffusion models in population dynamics. Ann. Probab. 37 (2009), no. 5, 1926--1969. MR2561437
  • Cattiaux, Patrick; Méléard, Sylvie. Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinction. J. Math. Biol. 60 (2010), no. 6, 797--829. MR2606515
  • Cavender, James A. Quasi-stationary distributions of birth-and-death processes. Adv. Appl. Probab. 10 (1978), no. 3, 570--586. MR0501388
  • Champagnat, Nicolas; Lambert, Amaury. Evolution of discrete populations and the canonical diffusion of adaptive dynamics. Ann. Appl. Probab. 17 (2007), no. 1, 102--155. MR2292582
  • Darroch, J. N.; Seneta, E. On quasi-stationary distributions in absorbing discrete-time finite Markov chains. J. Appl. Probability 2 1965 88--100. MR0179842
  • Darroch, J. N.; Seneta, E. On quasi-stationary distributions in absorbing continuous-time finite Markov chains. J. Appl. Probability 4 1967 192--196. MR0212866
  • Dunkl, Charles F.; Xu, Yuan. Orthogonal polynomials of several variables. Encyclopedia of Mathematics and its Applications, 81. Cambridge University Press, Cambridge, 2001. xvi+390 pp. ISBN: 0-521-80043-9 MR1827871
  • Ferrari, Pablo A.; Martínez, Servet; Picco, Pierre. Existence of nontrivial quasi-stationary distributions in the birth-death chain. Adv. in Appl. Probab. 24 (1992), no. 4, 795--813. MR1188953
  • Flaspohler, David C. Quasi-stationary distributions for absorbing continuous-time denumerable Markov chains. Ann. Inst. Statist. Math. 26 (1974), 351--356. MR0368155
  • Gantmacher, F. R. Matrizentheorie. (German) [Theory of matrices] With a foreword by D. P. Želobenko. Translated from the Russian by Helmut Boseck, Dietmar Soyka and Klaus Stengert. Hochschulbücher für Mathematik [University Books for Mathematics], 86. VEB Deutscher Verlag der Wissenschaften, Berlin, 1986. 654 pp. ISBN: 3-326-00001-4 MR0863127
  • Gosselin, Frédéric. Asymptotic behavior of absorbing Markov chains conditional on nonabsorption for applications in conservation biology. Ann. Appl. Probab. 11 (2001), no. 1, 261--284. MR1825466
  • Högnäs, Göran. On the quasi-stationary distribution of a stochastic Ricker model. Stochastic Process. Appl. 70 (1997), no. 2, 243--263. MR1475665
  • Karlin, S.; McGregor, J. Linear growth models with many types and multidimensional Hahn polynomials. Theory and application of special functions (Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975), pp. 261--288. Math. Res. Center, Univ. Wisconsin, Publ. No. 35, Academic Press, New York, 1975. MR0406574
  • Kesten, Harry. A ratio limit theorem for (sub) Markov chains on $\{1,2,\cdots\}$ with bounded jumps. Adv. in Appl. Probab. 27 (1995), no. 3, 652--691. MR1341881
  • Khare, Kshitij; Zhou, Hua. Rates of convergence of some multivariate Markov chains with polynomial eigenfunctions. Ann. Appl. Probab. 19 (2009), no. 2, 737--777. MR2521887
  • Kijima, Masaaki; Seneta, E. Some results for quasi-stationary distributions of birth-death processes. J. Appl. Probab. 28 (1991), no. 3, 503--511. MR1123824
  • M. Kimura, phThe neutral theory of molecular evolution, Cambridge University Press, 1983.
  • Motoo Kimura, phSolution of a process of random genetic drift with a continuous model, Proc. Nat. Acad. Sci. 41 (1955), 144--150.
  • Murray, J. D. Mathematical biology. Second edition. Biomathematics, 19. Springer-Verlag, Berlin, 1993. xiv+767 pp. ISBN: 3-540-57204-X MR1239892
  • Nåsell, Ingemar. On the quasi-stationary distribution of the stochastic logistic epidemic. Epidemiology, cellular automata, and evolution (Sofia, 1997). Math. Biosci. 156 (1999), no. 1-2, 21--40. MR1686454
  • P. K. Pollett, phQuasi-stationary distributions: A bibliography, available on, 2011.
  • Seneta, E.; Vere-Jones, D. On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states. J. Appl. Probability 3 1966 403--434. MR0207047
  • van Doorn, Erik A. Quasi-stationary distributions and convergence to quasi-stationarity of birth-death processes. Adv. in Appl. Probab. 23 (1991), no. 4, 683--700. MR1133722
  • Zettl, Anton. Sturm-Liouville theory. Mathematical Surveys and Monographs, 121. American Mathematical Society, Providence, RI, 2005. xii+328 pp. ISBN: 0-8218-3905-5 MR2170950

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.