Free Access
Issue
ESAIM: PS
Volume 12, April 2008
Page(s) 345 - 386
DOI https://doi.org/10.1051/ps:2007052
Published online 08 May 2008
  1. D. Aldous, Stopping times and tightness. Ann. Probab. 6 (1978) 335–340. [CrossRef] [Google Scholar]
  2. K.B. Athreya and P.E. Ney, Branching Processes. Springer edition (1970). [Google Scholar]
  3. R. Bellman and T.E. Harris, On age-dependent binary branching processes. Ann. Math. 55 (1952) 280–295. [CrossRef] [Google Scholar]
  4. P. Billingsley, Convergence of Probability Measures. John Wiley & Sons (1968). [Google Scholar]
  5. E. Bishop and R.R. Phelps, The support functionals of a convex set, in Proc. Sympos. Pure Math. Amer. Math. Soc., Ed. Providence 7 (1963) 27–35. [Google Scholar]
  6. S. Busenberg and M. Iannelli, A class of nonlinear diffusion problems in age-dependent population dynamics. Nonlinear Anal. 7 (1983) 501–529. [CrossRef] [MathSciNet] [Google Scholar]
  7. N. Champagnat, R. Ferrière and S. Méléard, Individual-based probabilistic models of adpatative evolution and various scaling approximations, in Proceedings of the 5th seminar on Stochastic Analysis, Random Fields and Applications, Probability in Progress Series, Ascona, Suisse (2006). Birkhauser. [Google Scholar]
  8. N. Champagnat, R. Ferrière and S. Méléard, Unifying evolutionary dynamics: from individual stochastic processes to macroscopic models via timescale separation. Theoretical Population Biology (2006). [Google Scholar]
  9. K.S. Crump and C.J. Mode, A general age-dependent branching process i. J. Math. Anal. Appl. 24 (1968) 494–508. [CrossRef] [Google Scholar]
  10. K.S. Crump and C.J. Mode, A general age-dependent branching process ii. J. Math. Anal. Appl. 25 (1969) 8–17. [CrossRef] [Google Scholar]
  11. D.A. Dawson and J. Gärtner, Large deviations from the McKean-Vlasov limit for weakly interacting diffusions. Stochastics 20 (1987) 247–308. [CrossRef] [MathSciNet] [Google Scholar]
  12. A. Dembo and O. Zeitouni, Large Deviation Techniques and Applications. Jones and Bartlett Publishers, Boston (1993). [Google Scholar]
  13. R.A. Doney, Age-dependent birth and death processes. Z. Wahrscheinlichkeitstheorie verw. 22 (1972) 69–90. [CrossRef] [Google Scholar]
  14. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. North-Holland, Amsterdam (1976). [Google Scholar]
  15. L.C. Evans, Partial Differential Equations, Grad. Stud. Math. 19 American Mathematical Society (1998). [Google Scholar]
  16. H. Von Foerster, Some remarks on changing populations, in The Kinetics of Cellular Proliferation, Grune & Stratton Ed., New York (1959) 382–407. [Google Scholar]
  17. N. Fournier and S. Méléard, A microscopic probabilistic description of a locally regulated population and macroscopic approximations. Ann. Appl. Probab. 14 (2004) 1880–1919. [CrossRef] [MathSciNet] [Google Scholar]
  18. M.I. Freidlin and A. Ventzell, Random Perturbations of Dynamical Systems. Springer-Verlag (1984). [Google Scholar]
  19. F. Galton and H.W. Watson, On the probability of the extinction of families. J. Anthropol. Inst. Great B. and Ireland 4 (1874) 138–144. [Google Scholar]
  20. C. Graham and S. Méléard, A large deviation principle for a large star-shaped loss network with links of capacity one. Markov Processes and Related Fields 3 (1997) 475–492. [MathSciNet] [Google Scholar]
  21. C. Graham and S. Méléard, An upper bound of large deviations for a generalized star-shaped loss network. Markov Processes and Related Fields 3 (1997) 199–224. [MathSciNet] [Google Scholar]
  22. M.E. Gurtin and R.C. MacCamy, Nonlinear age-dependent population dynamics. Arch. Rat. Mech. Anal. 54 (1974) 281–300. [Google Scholar]
  23. T.E. Harris, The Theory of Branching Processes. Springer, Berlin (1963). [Google Scholar]
  24. R.B. Israel, Existence of phase transitions for long-range interactions. Comm. Math. Phys. 43 (1975) 59–68. [CrossRef] [MathSciNet] [Google Scholar]
  25. J. Jacod and A.N. Shiryaev, Limit Theorems for Stochastic Processes. Springer-Verlag, Berlin (1987). [Google Scholar]
  26. P. Jagers, A general stochastic model for population development. Skand. Aktuarietidskr 52 (1969) 84–103. [Google Scholar]
  27. P. Jagers and F. Klebaner, Population-size-dependent and age-dependent branching processes. Stochastic Process Appl. 87 (2000) 235–254. [CrossRef] [MathSciNet] [Google Scholar]
  28. A. Jakubowski, On the skorokhod topology. Ann. Inst. H. Poincaré 22 (1986) 263–285. [Google Scholar]
  29. A. Joffe and M. Métivier, Weak convergence of sequences of semimartingales with applications to multitype branching processes. Advances in Applied Probability 18 (1986) 20–65. [CrossRef] [MathSciNet] [Google Scholar]
  30. D.G. Kendall, Stochastic processes and population growth. J. Roy. Statist. Sec., Ser. B 11 (1949) 230–264. [Google Scholar]
  31. C. Kipnis and C. Léonard, Grandes déviations pour un système hydrodynamique asymétrique de particules indépendantes. Ann. Inst. H. Poincaré 31 (1995) 223–248. [Google Scholar]
  32. C. Léonard, On large deviations for particle systems associated with spatially homogeneous boltzmann type equations. Probab. Theory Related Fields 101 (1995) 1–44. [CrossRef] [MathSciNet] [Google Scholar]
  33. T.R. Malthus, An Essay on the Principle of Population. J. Johnson St. Paul's Churchyard (1798). [Google Scholar]
  34. P. Marcati, On the global stability of the logistic age dependent population growth. J. Math. Biol. 15 (1982) 215–226. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  35. A.G. McKendrick, Applications of mathematics to medical problems. Proc. Edin. Math. Soc. 54 (1926) 98–130. [Google Scholar]
  36. S. Méléard and S. Roelly, Sur les convergences étroite ou vague de processus à valeurs mesures. C.R. Acad. Sci. Paris, Série I 317 (1993) 785–788. [Google Scholar]
  37. S. Méléard and V.C. Tran. Age-structured trait substitution sequence process and canonical equation. Submitted. [Google Scholar]
  38. S.P. Meyn and R.L. Tweedie, Stability of markovian processes iii: Foster-lyapunov criteria for continuous-time processes. Advances in Applied Probability 25 (1993) 518–548. [CrossRef] [MathSciNet] [Google Scholar]
  39. K. Oelschläger, Limit theorem for age-structured populations. Ann. Probab. (1990). [Google Scholar]
  40. G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions. Cambridge Uiversity Press (1992). [Google Scholar]
  41. S.T. Rachev, Probability Metrics and the Stability of Stochastic Models, John Wiley & Sons (1991). [Google Scholar]
  42. M.M. Rao and Z.D. Ren, Theory of Orlicz spaces. M. Dekker, New York (1991). [Google Scholar]
  43. S. Roelly, A criterion of convergence of measure-valued processes: Application to measure branching processes. Stochastics 17 (1986) 43–65. [MathSciNet] [Google Scholar]
  44. W. Rudin, Real and Complex Analysis. McGraw-Hill International Editions, third edition (1987). [Google Scholar]
  45. F.R. Sharpe and A.J. Lotka, A problem in age distribution. Philos. Mag. 21 (1911) 435–438. [Google Scholar]
  46. W. Solomon, Representation and approximation of large population age distributions using poisson random measures. Stochastic Process. Appl. 26 (1987) 237–255. [CrossRef] [MathSciNet] [Google Scholar]
  47. V.C. Tran, Modèles particulaires stochastiques pour des problèmes d'évolution adaptative et pour l'approximation de solutions statistiques. Ph.D. thesis, Université Paris X - Nanterre. http://tel.archives-ouvertes.fr/tel-00125100. [Google Scholar]
  48. P.F. Verhulst, Notice sur la loi que la population suit dans son accroissement. Correspondance Mathématique et Physique 10 (1838) 113–121. [Google Scholar]
  49. C. Villani, Topics in Optimal Transportation. American Mathematical Society (2003). [Google Scholar]
  50. F.J.S. Wang, A central limit theorem for age- and density-dependent population processes. Stochastic Process. Appl. 5 (1977) 173–193. [CrossRef] [Google Scholar]
  51. G.F. Webb, Theory of Nonlinear Age-Dependent Population Dynamics, Monographs and Textbooks in Pure and Applied mathematics 89, Marcel Dekker, inc., New York-Basel (1985). [Google Scholar]
  52. C. Zuily and H. Queffélec, Éléments d'analyse pour l'agrégation. Masson (1995). [Google Scholar]

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