Population dynamics: Poisson approximation and its relation to the Langevin process.
We discuss how to simulate a stochastic evolution process in terms of difference equations with Poisson distributions of independent events when the problem is naturally described by discrete variables. For large populations the Poisson approximation becomes a discrete integration of the Langevin approximation [T. G. Kurtz, J. Appl. Prob. 7, 49 (1970); 8, 344 (1971)]. We analyze when the latter gives a reasonable representation of the original evolution for finite size systems. A simple example of an epidemic process is used to organize the discussion and to perform statistical tests that underline the goodness of the proposed method.
Aparicio
J P
JP
Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, 1428 Buenos Aires, Argentina. jpa9@cornell.edu
Solari
H G
HG
D016012:Poisson Distribution; D011157:Population Dynamics; D013269:Stochastic Processes