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References
- O.O. Aalen, H.K. Gjessing. Understanding the shape of the hazard rate: a process point of view. With comments and a rejoinder by the authors. Statist. Sci. 16 (2001), no. 1, 1--22. Math. Review 2002e:62095
- G. Allaire. Analyse numérique et optimisation. (2005) Éditions de l'École Polytechnique.
- I. Ben-Ari, R.G. Pinsky. Ergodic behavior of diffusions with random jumps from the boundary. Stochastic Process. Appl. 119 (2009), no. 3, 864--881. Math. Review 2010d:60177
- K. Burdzy, R. Holyst, D. Ingerman and P. March. Configurational transition in a fleming-viot-type model and probabilistic interpretation of laplacian eigenfunctions. J. Phys. A 29 (1996) 2633--2642.
- K. Burdzy, R. Hołyst, P. March, Peter. A Fleming-Viot particle representation of the Dirichlet Laplacian. Comm. Math. Phys. 214 (2000), no. 3, 679--703. Math. Review 2002c:60130
- P. Cattiaux, P. Collet, A. Lambert, S. Martínez, S. Méléard, J. San Martín. Quasi-stationary distributions and diffusion models in population dynamics. Ann. Probab. 37 (2009), no. 5, 1926--1969. Math. Review 2011b:60314
- P. Cattiaux, Patrick, S. Méléard. Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinction. J. Math. Biol. 60 (2010), no. 6, 797--829. Math. Review 2011a:92067
- J.A. Cavender, Quasi-stationary distributions of birth-and-death processes. Adv. Appl. Probab. 10 (1978), no. 3, 570--586. Math. Review 58 #18754
- M. Chaleyat-Maurel and N. El Karoui. Un problème de réflexion et ses applications au temps local et aux équations différentielles stochastiques sur R. Cas continu. Astérisque 52-53 (1978) 117--144.
- P. Collet, S. Martínez, J. San Martín, Jaime. Asymptotic laws for one-dimensional diffusions conditioned to nonabsorption.
- Ann. Probab. 23 (1995), no. 3, 1300--1314. Math. Review 96i:60083
- J.N. Darroch, E. Seneta. On quasi-stationary distributions in absorbing discrete-time finite Markov chains. J. Appl. Probability 2 (1965) 88--100. Math. Review 31 #4083.
- M.C Delfour, J.-P. Zolésio. Shapes and geometries. Analysis, differential calculus, and optimization. Advances in Design and Control 4 (2001) Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, xviii+482 pp. ISBN: 0-89871-489-3 Math. Review 2002i:49002
- D. Down, S.P. Meyn, R.L. Tweedie Exponential and uniform ergodicity of Markov processes. Ann. Probab. 23 (1995), no. 4, 1671--1691. Math. Review 97c:60181
- S.N. Ethier, T.G. Kurtz Markov processes. Characterization and convergence. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. (1986) John Wiley & Sons, Inc., New York, x+534 pp. ISBN: 0-471-08186-8 Math. Review 88a:60130
- P.A. Ferrari, H. Kesten, S. Martinez, P. Picco. Existence of quasi-stationary distributions. A renewal dynamical approach.
- Ann. Probab. 23 (1995), no. 2, 501--521. Math. Review 96c:60089
- P.A. Ferrari, N. Marić. Quasi stationary distributions and Fleming-Viot processes in countable spaces. Electron. J. Probab. 12 (2007), no. 24, 684--702. Math. Review 2008b:60213
- G.L. Gong, M.P. Qian, Z.X. Zhao. Killed diffusions and their conditioning. Probab. Theory Related Fields 80 (1988), no. 1, 151--167. Math. Review 90c:60051
- I. Grigorescu, M. Kang. Hydrodynamic limit for a Fleming-Viot type system. Stochastic Process. Appl. 110 (2004), no. 1, 111--143. Math. Review 2005d:60153
- I. Grigorescu, M. Kang. Ergodic properties of multidimensional Brownian motion with rebirth. Electron. J. Probab. 12 (2007), no. 48, 1299--1322. Math. Review 2008j:60186
- I. Grigorescu, M. Kang. Immortal particle for a catalytic branching process. To appear in Probab. Theory Related Fields
- T. Huillet. On Wright Fisher diffusion and its relatives. Journal of Statistical Mechanics: Theory and Experiment 11 (2007)
- A. Jakubowski. Tightness criteria for random measures with application to the principle of conditioning in Hilbert spaces. Probab. Math. Statist. 9 (1988), no. 1, 95--114. Math. Review 89h:60003
- M. Kolb, D. Steinsaltz. Quasilimiting behavior for one-dimensional diffusions with killing. To appear in Annals of Probability
- M. Kolb, A. Wübker. On the Spectral Gap of Brownian Motion with Jump Boundary. To appear in Electronic Journal of Probability
- M. Kolb, A. Wübker. Spectral Analysis of Diffusions with Jump Boundary. To appear in Journal of Functional Analysis
- T. Li and J.J. Anderson. The vitality model: A way to understand population survival and demographic heterogeneity. Theoretical Population Biology 76 (2009) no. 2, 118 -- 131.
- M. Lladser, J. San Martín. Domain of attraction of the quasi-stationary distributions for the Ornstein-Uhlenbeck process. J. Appl. Probab. 37 (2000), no. 2, 511--520. Math. Review 2003b:60011
- J.-U. Löbus. A stationary Fleming-Viot type Brownian particle system. Math. Z. 263 (2009), no. 3, 541--581. Math. Review 2010m:60344
- S. Martinez, P. Picco, J. San Martin. Domain of attraction of quasi-stationary distributions for the Brownian motion with drift. Adv. in Appl. Probab. 30 (1998), no. 2, 385--408. Math. Review 99i:60156
- I. Nåsell. Extinction and quasi-stationarity in the verhulst logistic model. Journal of Theoretical Biology 211 (2001), no. 1, 11 -- 27.
- P. Polett. Quasi-stationary distributions : a bibliography. http://www.maths.uq .edu.au/$sim$pkp/papers/qsds/qsds.pdf.
- E. Priola, F.-Y. Wang. Gradient estimates for diffusion semigroups with singular coefficients. J. Funct. Anal. 236 (2006), no. 1, 244--264. Math. Review 2007i:47052
- D. Revuz, M. Yor. Continuous martingales and Brownian motion. Third edition. Grundlehren der Mathematischen Wissenschaften, 293. Springer-Verlag, Berlin, (1999). xiv+602 pp. ISBN: 3-540-64325-7 Math. Review 2000h:60050.
- D. Steinsaltz, S.N. Evans. Markov mortality models: Implications of quasistationarity and varying initial conditions. Theo. Pop. Bio. 65 (2004), 319--337.
- A.M. Yaglom. Certain limit theorems of the theory of branching random processes. (Russian) Doklady Akad. Nauk SSSR (N.S.) 56 (1947), 795--798. Math. Review 9,149e
- K. Yosida. Functional analysis. Second edition. Die Grundlehren der mathematischen Wissenschaften, 123 Springer-Verlag New York Inc., New York. (1968), xii+465 pp. Math. Review 39 #741

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