Convergence of stochastic gene networks to hybrid piecewise deterministic processes

By A. Crudu, Arnaud Debussche, Aurelien Muller, O. Radulescu. 2011

137 citations recorded by the source corpus.

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.

Subfields: Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/b4eb4a7247b70f4b4f63540dd3481e161d07328b

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In Modeling and Simulation

1. Bertrand Cloez
2. Florent Malrieu
3. Martin Hairer
4. Jinghai Shao

In Molecular Biology

1. Bertrand Cloez
2. Martin Hairer
3. Jinghai Shao

Citations in the corpus

• Some simple but challenging Markov processes (2014, background): “In particular, they naturally appear as the approximation of Markov chains mixing slow and fast dynamics (see [19]).”
• Exponential ergodicity for Markov processes with random switching (2013, background): “g; piecewise deterministic Markov process; switching; Wasserstein distance 1. Introduction Markov processes with switching are intensively used for modelling purposes in applied subjects like biology [10, 12, 16], storage modelling [7], neuronal activity [17, 31]. This class of Markov processes is r”
• Criteria for transience and recurrence of regime-switching diffusion processes * (2014, background): “[5, 7, 8, 16] and references therein for more details on their application.”
• Ergodicity of regime-switching diffusions in Wasserstein distances (2014, background): “We refer the reader to [9, 10, 12, 11, 21] and references therein for more details of regime-switching diffusion processes and their applications.”