Free Access
Volume 12, April 2008
Page(s) 345 - 386
Published online 08 May 2008
  1. D. Aldous, Stopping times and tightness. Ann. Probab. 6 (1978) 335–340. [CrossRef]
  2. K.B. Athreya and P.E. Ney, Branching Processes. Springer edition (1970).
  3. R. Bellman and T.E. Harris, On age-dependent binary branching processes. Ann. Math. 55 (1952) 280–295. [CrossRef]
  4. P. Billingsley, Convergence of Probability Measures. John Wiley & Sons (1968).
  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.
  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]
  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.
  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).
  9. K.S. Crump and C.J. Mode, A general age-dependent branching process i. J. Math. Anal. Appl. 24 (1968) 494–508. [CrossRef]
  10. K.S. Crump and C.J. Mode, A general age-dependent branching process ii. J. Math. Anal. Appl. 25 (1969) 8–17. [CrossRef]
  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]
  12. A. Dembo and O. Zeitouni, Large Deviation Techniques and Applications. Jones and Bartlett Publishers, Boston (1993).
  13. R.A. Doney, Age-dependent birth and death processes. Z. Wahrscheinlichkeitstheorie verw. 22 (1972) 69–90. [CrossRef]
  14. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. North-Holland, Amsterdam (1976).
  15. L.C. Evans, Partial Differential Equations, Grad. Stud. Math. 19 American Mathematical Society (1998).
  16. H. Von Foerster, Some remarks on changing populations, in The Kinetics of Cellular Proliferation, Grune & Stratton Ed., New York (1959) 382–407.
  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]
  18. M.I. Freidlin and A. Ventzell, Random Perturbations of Dynamical Systems. Springer-Verlag (1984).
  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.
  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]
  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]
  22. M.E. Gurtin and R.C. MacCamy, Nonlinear age-dependent population dynamics. Arch. Rat. Mech. Anal. 54 (1974) 281–300.
  23. T.E. Harris, The Theory of Branching Processes. Springer, Berlin (1963).
  24. R.B. Israel, Existence of phase transitions for long-range interactions. Comm. Math. Phys. 43 (1975) 59–68. [CrossRef] [MathSciNet]
  25. J. Jacod and A.N. Shiryaev, Limit Theorems for Stochastic Processes. Springer-Verlag, Berlin (1987).
  26. P. Jagers, A general stochastic model for population development. Skand. Aktuarietidskr 52 (1969) 84–103.
  27. P. Jagers and F. Klebaner, Population-size-dependent and age-dependent branching processes. Stochastic Process Appl. 87 (2000) 235–254. [CrossRef] [MathSciNet]
  28. A. Jakubowski, On the skorokhod topology. Ann. Inst. H. Poincaré 22 (1986) 263–285.
  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]
  30. D.G. Kendall, Stochastic processes and population growth. J. Roy. Statist. Sec., Ser. B 11 (1949) 230–264.
  31. C. Kipnis and C. Léonard, Grandes déviations pour un système hydrodynamique asymétrique de particules indépendantes. Ann. Inst. H. Poincaré 31 (1995) 223–248.
  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]
  33. T.R. Malthus, An Essay on the Principle of Population. J. Johnson St. Paul's Churchyard (1798).
  34. P. Marcati, On the global stability of the logistic age dependent population growth. J. Math. Biol. 15 (1982) 215–226. [CrossRef] [MathSciNet] [PubMed]
  35. A.G. McKendrick, Applications of mathematics to medical problems. Proc. Edin. Math. Soc. 54 (1926) 98–130.
  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.
  37. S. Méléard and V.C. Tran. Age-structured trait substitution sequence process and canonical equation. Submitted.
  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]
  39. K. Oelschläger, Limit theorem for age-structured populations. Ann. Probab. (1990).
  40. G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions. Cambridge Uiversity Press (1992).
  41. S.T. Rachev, Probability Metrics and the Stability of Stochastic Models, John Wiley & Sons (1991).
  42. M.M. Rao and Z.D. Ren, Theory of Orlicz spaces. M. Dekker, New York (1991).
  43. S. Roelly, A criterion of convergence of measure-valued processes: Application to measure branching processes. Stochastics 17 (1986) 43–65. [MathSciNet]
  44. W. Rudin, Real and Complex Analysis. McGraw-Hill International Editions, third edition (1987).
  45. F.R. Sharpe and A.J. Lotka, A problem in age distribution. Philos. Mag. 21 (1911) 435–438.
  46. W. Solomon, Representation and approximation of large population age distributions using poisson random measures. Stochastic Process. Appl. 26 (1987) 237–255. [CrossRef] [MathSciNet]
  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.
  48. P.F. Verhulst, Notice sur la loi que la population suit dans son accroissement. Correspondance Mathématique et Physique 10 (1838) 113–121.
  49. C. Villani, Topics in Optimal Transportation. American Mathematical Society (2003).
  50. F.J.S. Wang, A central limit theorem for age- and density-dependent population processes. Stochastic Process. Appl. 5 (1977) 173–193. [CrossRef]
  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).
  52. C. Zuily and H. Queffélec, Éléments d'analyse pour l'agrégation. Masson (1995).

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.