Stochastic population dynamics: The Poisson approximation

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 67, Issue 3 1, 2003, Pages

  Solari, Hernán G ^a   Natiello, Mario A ^b  

^a UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^b LUND UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; MARKOV PROCESSES; MONTE CARLO METHODS; ORDINARY DIFFERENTIAL EQUATIONS; POISSON DISTRIBUTION; THEOREM PROVING;

POISSON APPROXIMATION; STOCHASTIC POPULATION DYNAMICS;

STATISTICAL MECHANICS;

EID: 42749103363     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations (Wiley, London, 1971).
2. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York, 1975).
3. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems (Wiley, New York, 1977).
4. D. T. Gillespie, J. Phys. Chem. 81, 2340 (1977).
5. J. Güémez and M.A. Matías, Phys. Rev. E 51, 3059 (1995).
6. C.H. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
7. C.H. Henry, IEEE J. Quantum Electron. 19, 1391 (1983).
8. W.W. Chow, S.W. Koch, and M. Sargent, Semiconductor-Laser Physics (Springer-Verlag, Berlin, 1994).
9. E. Renshaw, Modelling Biological Populations in Space and Time (Cambridge University Press, Cambridge, 1991).
10. S.N. Ethier and T.G. Kurtz, Markov Processes (Wiley, New York, 1986).
11. T.G. Kurtz, J. Appl. Probab. 7, 49 (1970).
12. T.G. Kurtz, J. Appl. Probab. 8, 344 (1971).
13. H. Andersson and T. Britton, Stochastic Epidemic Models and Their Statistical Analysis, Lecture Notes in Statistics Vol. 151 (Springer-Verlag, Berlin, 2000).
14. J.P. Aparicio and H.G. Solari, Phys. Rev. Lett. 86, 4183 (2001).
15. A. Renyi, Cálculo de Probabilidades (Editorial Reverté, Madrid, 1976).
16. Situations in which the probability of occurrence of an event depends on the history of the individuals are usually handled by introducing subpopulations. For example, if the time required to reach sexual maturity is relevant, we can introduce an age-structured population: only the sexually mature subpopulation will be involved in reproductive events.