Skip to Main content Skip to Navigation
Theses

Approximations hybrides de processus de Markov à sauts multi-échelles : applications aux modèles de réseaux de gènes en biologie moléculaire

Abstract : The main goal of this thesis was to develop new mathematical tools for the study of the stochastic phenomena in molecular biology. The mathematical models used to describe the stochastic behaviour of a system of biochemical reactions are based on Markov jumps processes. We propose hybrid approximations for multi-scale Markov jumps processes. These approximations are obtained by partial Kramers-Moyal expansion which is equivalent to the application of the central limit theorem to a sub-model. Thus, different approximations are obtained: piecewise deterministic processes and hybrid diffusions. These processes are simulated with suitable numerical algorithms. Furthermore, we show the weak convergence of Markov jump processes to piecewise deterministic processes with or without jumps in the continuous variables. The hybrid approximations can be simplified even more by averaging. We propose some results for this type of reduction of the process.
Document type :
Theses
Complete list of metadatas

Cited literature [12 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00454886
Contributor : Alina Crudu <>
Submitted on : Tuesday, February 9, 2010 - 2:01:06 PM
Last modification on : Thursday, January 7, 2021 - 4:25:27 PM
Long-term archiving on: : Friday, June 18, 2010 - 7:41:08 PM

Identifiers

  • HAL Id : tel-00454886, version 1

Citation

Alina Crudu. Approximations hybrides de processus de Markov à sauts multi-échelles : applications aux modèles de réseaux de gènes en biologie moléculaire. Mathématiques [math]. Université Rennes 1, 2009. Français. ⟨tel-00454886⟩

Share

Metrics

Record views

604

Files downloads

1054