Population dynamics: a Poisson approximation and its relation to the Langevin process

APARICIO, JUAN PABLO; SOLARI, HERNAN

PHYSICAL REVIEW LETTERS

American Physical Association

Año: 2001 vol. 86 p. 4183 - 4186

0031-9007

We discuss how to simulate a stochastic evolution process in terms of difference equations with Poissondistributions of independent events when the problem is naturally described by discrete variables. Forlarge 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 givesa reasonable representation of the original evolution for finite size systems. A simple example of anepidemic process is used to organize the discussion and to perform statistical tests that underline thegoodness of the proposed method.