Convergence of stochastic gene networks to hybrid piecewise deterministic processes

Alina Crudu; Arnaud Debussche; Aurélie Muller; Ovidiu Radulescu

doi:10.48550/arxiv.1101.1431

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Convergence of stochastic gene networks to hybrid piecewise deterministic processes

Alina Crudu, Arnaud Debussche, Aurélie Muller et Ovidiu Radulescu

07/01/2011

DOI: https://doi.org/10.48550/arxiv.1101.1431

Résumé

Mathematics - Probability

We study the asymptotic behavior of multiscale stochastic gene networks using weak limits of Markov jump processes. Depending on the time and concentration scales of the system we distinguish four types of limits: continuous piecewise deterministic processes (PDP) with switching, PDP with jumps in the continuous variables, averaged PDP, and PDP with singular switching. We justify rigorously the convergence for the four types of limits. The convergence results can be used to simplify the stochastic dynamics of gene network models arising in molecular biology.

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Détails

Titre: Convergence of stochastic gene networks to hybrid piecewise deterministic processes
Créateurs - sans rôle: Alina Crudu - IRMAR
Arnaud Debussche - IRMAR
Aurélie Muller - IECN
Ovidiu Radulescu
Identifiants: 99147640809311
Unité académique: Laboratory of Pathogens and Host Immunity - LPHI
Langue: English
Type de ressource: Preprint