A Piecewise Deterministic Limit for a Multiscale Stochastic Spatial Gene Network - Centre Henri Lebesgue Accéder directement au contenu
Article Dans Une Revue Applied Mathematics and Optimization Année : 2021

A Piecewise Deterministic Limit for a Multiscale Stochastic Spatial Gene Network

Résumé

We consider multiscale stochastic spatial gene networks involving chemical reactions and diffusions. The model is Markovian and the transitions are driven by Poisson random clocks. We consider a case where there are two different spatial scales: a microscopic one with fast dynamic and a macroscopic one with slow dynamic. At the microscopic level, the species are abundant and for the large population limit a partial differential equation (PDE) is obtained. On the contrary at the macroscopic level, the species are not abundant and their dynamic remains governed by jump processes. It results that the PDE governing the fast dynamic contains coefficients which randomly change. The global weak limit is an infinite dimensional continuous piecewise deterministic Markov process (PDMP). Also, we prove convergence in the supremum norm.
Fichier principal
Vignette du fichier
MSSM_Hybrid_Limit_Supremum_Norm_2.pdf (365.5 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02894345 , version 1 (09-07-2020)

Identifiants

Citer

Arnaud Debussche, Mac Jugal Nguepedja Nankep. A Piecewise Deterministic Limit for a Multiscale Stochastic Spatial Gene Network. Applied Mathematics and Optimization, 2021, 84 (S2), pp.1731-1767. ⟨10.1007/s00245-021-09809-0⟩. ⟨hal-02894345⟩
61 Consultations
35 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More