A continuous measure-valued model is obtained as the limit of discrete finite-dimensional Markov processes describing the evolution of a population of interacting cells (classified by their DNA content), as the initial number of individuals diverges and the DNA production unit tends independently to zero. The limit is identified by a nonlinear evolution equation, which is shown to have a unique solution by a contraction argument in a suitable metric space. In the critical case the solution of the limit equation can be viewed as the family of the one-time probability distributions of a nonlinear Markov process.
Calzolari, A., Costantini, C., Gerardi, A. (1991). Law of large numbers for DNA distribution in an interacting cell population. SIAM JOURNAL ON APPLIED MATHEMATICS, 51(1), 150-159 [10.1080/17442509608834052].
Law of large numbers for DNA distribution in an interacting cell population
CALZOLARI, ANTONELLA;
1991-02-01
Abstract
A continuous measure-valued model is obtained as the limit of discrete finite-dimensional Markov processes describing the evolution of a population of interacting cells (classified by their DNA content), as the initial number of individuals diverges and the DNA production unit tends independently to zero. The limit is identified by a nonlinear evolution equation, which is shown to have a unique solution by a contraction argument in a suitable metric space. In the critical case the solution of the limit equation can be viewed as the family of the one-time probability distributions of a nonlinear Markov process.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
