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.
feb-1991
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
English
Con Impact Factor ISI
Filtering, Counting process, Jump Markov Process, Approximation, Coupling
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].
Calzolari, A; Costantini, C; Gerardi, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/41242
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