Uniform convergence of solutions to stochastic hybrid models of gene regulatory networks
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916302602371072 |
|---|---|
| author | Dobrick, Alexander Hölz, Julian |
| author_facet | Dobrick, Alexander Hölz, Julian |
| contents | In a recent paper by Kurasov, Lück, Mugnolo and Wolf, a hybrid gene regulatory network was proposed to model gene expression dynamics by using a stochastic system of coupled partial differential equations. This approach approximates protein counts in cells by modelling them as distributions. In a follow-up paper, the existence and strong convergence of the solutions to equilibrium was proven. In this paper, we make use of a recent convergence theorem for stochastic, irreducible semigroups that contain partial integral operators. In particular, we improve upon their results by showing that the convergence rate is independent of the initial distribution of proteins, therefore proving that the solutions converge not only strongly but even uniformly to equilibrium. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_07435 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniform convergence of solutions to stochastic hybrid models of gene regulatory networks Dobrick, Alexander Hölz, Julian Functional Analysis Probability Spectral Theory 35B40, 47D06, 47D07 In a recent paper by Kurasov, Lück, Mugnolo and Wolf, a hybrid gene regulatory network was proposed to model gene expression dynamics by using a stochastic system of coupled partial differential equations. This approach approximates protein counts in cells by modelling them as distributions. In a follow-up paper, the existence and strong convergence of the solutions to equilibrium was proven. In this paper, we make use of a recent convergence theorem for stochastic, irreducible semigroups that contain partial integral operators. In particular, we improve upon their results by showing that the convergence rate is independent of the initial distribution of proteins, therefore proving that the solutions converge not only strongly but even uniformly to equilibrium. |
| title | Uniform convergence of solutions to stochastic hybrid models of gene regulatory networks |
| topic | Functional Analysis Probability Spectral Theory 35B40, 47D06, 47D07 |
| url | https://arxiv.org/abs/2305.07435 |