Skip to main content
Top

2015 | OriginalPaper | Chapter

3. Scaling Limits for Birth and Death Processes

Authors : Vincent Bansaye, Sylvie Méléard

Published in: Stochastic Models for Structured Populations

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

If the population is large, so many birth and death events occur that the dynamics becomes difficult to describe individual per individual. Living systems need resources in order to survive and reproduce and the biomass per capita depends on the order of magnitude of these resources.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference D. Aldous. Stopping times and tightness. Ann. Probab. 6, 335–340, 1978. D. Aldous. Stopping times and tightness. Ann. Probab. 6, 335–340, 1978.
12.
go back to reference C. Boeinghoff and M. Hutzenthaler. Branching diffusions in random environment. Markov Proc. Rel. Fields, 18(2):269–310, 2012. C. Boeinghoff and M. Hutzenthaler. Branching diffusions in random environment. Markov Proc. Rel. Fields, 18(2):269–310, 2012.
29.
go back to reference A. Etheridge: Survival and extinction in a locally regulated population. Ann. Appl. Probab. 14, 188–214, 2004. A. Etheridge: Survival and extinction in a locally regulated population. Ann. Appl. Probab. 14, 188–214, 2004.
30.
go back to reference S. N. Ethier and T. G. Kurtz. Markov processes: characterization and convergence. Wiley, 1986. S. N. Ethier and T. G. Kurtz. Markov processes: characterization and convergence. Wiley, 1986.
34.
go back to reference S. N. Evans, A. Hening & S. Schreiber. Protected polymorphisms and evolutionary stability of patch-selection strategies in stochastic environments. In press, Journal of Mathematical Biology. S. N. Evans, A. Hening & S. Schreiber. Protected polymorphisms and evolutionary stability of patch-selection strategies in stochastic environments. In press, Journal of Mathematical Biology.
41.
go back to reference N. Ikeda and S. Watanabe. Stochastic differential equations and diffusion processes, 2nd ed. North-Holland, 1989. N. Ikeda and S. Watanabe. Stochastic differential equations and diffusion processes, 2nd ed. North-Holland, 1989.
43.
go back to reference A. Joffe and M. Métivier. Weak convergence of sequences of semimartingales with applications to multitype branching processes. Adv. Appl. Probab. 18, 20–65, 2012. A. Joffe and M. Métivier. Weak convergence of sequences of semimartingales with applications to multitype branching processes. Adv. Appl. Probab. 18, 20–65, 2012.
45.
go back to reference I. Karatzas and S.E. Shreve. Brownian Motion and Stochastic Calculus, 2nd ed. Springer, 1998. I. Karatzas and S.E. Shreve. Brownian Motion and Stochastic Calculus, 2nd ed. Springer, 1998.
51.
go back to reference A. Lambert. The branching process with logistic growth. Ann. Appl. Probab., 15 no.2, 150–1535, 2005. A. Lambert. The branching process with logistic growth. Ann. Appl. Probab., 15 no.2, 150–1535, 2005.
Metadata
Title
Scaling Limits for Birth and Death Processes
Authors
Vincent Bansaye
Sylvie Méléard
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-21711-6_3