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

References

  • Arrigoni, Francesca. Deterministic approximation of a stochastic metapopulation model. Adv. in Appl. Probab. 35 (2003), no. 3, 691--720. MR1990610
  • Barbour, A. D.; Luczak, M. J. Laws of large numbers for epidemic models with countably many types. Ann. Appl. Probab. 18 (2008), no. 6, 2208--2238. MR2473655
  • Barbour, A. D.; Luczak, M. J. A law of large numbers approximation for Markov population processes with countably many types. Probab. Theory Related Fields 153 (2012), no. 3-4, 727--757. MR2948691
  • Eibeck, Andreas; Wagner, Wolfgang. Stochastic interacting particle systems and nonlinear kinetic equations. Ann. Appl. Probab. 13 (2003), no. 3, 845--889. MR1994039
  • Kimmel, Marek; Axelrod, David E. Branching processes in biology. Interdisciplinary Applied Mathematics, 19. Springer-Verlag, New York, 2002. xviii+230 pp. ISBN: 0-387-95340-X MR1903571
  • Komlós, J.; Major, P.; Tusnády, G. An approximation of partial sums of independent ${\rm RV}$'s and the sample ${\rm DF}$. I. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 32 (1975), 111--131. MR0375412
  • Kretzschmar, Mirjam. Comparison of an infinite-dimensional model for parasitic diseases with a related 2-dimensional system. J. Math. Anal. Appl. 176 (1993), no. 1, 235--260. MR1222167
  • Kurtz, Thomas G. Solutions of ordinary differential equations as limits of pure jump Markov processes. J. Appl. Probability 7 1970 49--58. MR0254917
  • Kurtz, T. G. Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. J. Appl. Probability 8 1971 344--356. MR0287609
  • Levins, R.: Some demographic and genetic consequences of environmental heterogeneity for biological control. Bull. Entomol. Soc. Amer./ ol15 (1969), 237--240.
  • Luchsinger, C. J. Stochastic models of a parasitic infection, exhibiting three basic reproduction ratios. J. Math. Biol. 42 (2001), no. 6, 532--554. MR1845591
  • Luchsinger, C. J. Approximating the long-term behaviour of a model for parasitic infection. J. Math. Biol. 42 (2001), no. 6, 555--581. MR1845592
  • Pazy, A. Semigroups of linear operators and applications to partial differential equations. Applied Mathematical Sciences, 44. Springer-Verlag, New York, 1983. viii+279 pp. ISBN: 0-387-90845-5 MR0710486
  • Ricker, W. E.: Stock and Recruitment. J. Fisheries Res. Board Canada/ 11, (1954), 559--623.
  • Verhulst, P.-F.: Notice sur la loi que la population poursuit dans son accroissement. Correspondance Mathématique et Physique/ 10, (1838), 113--121.


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