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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(More)
Markov jump processes can model stochastic phenomena in molecular biology. Nevertheless , there are few mathematical results on the dynamics of these processes in their full generality. Furthermore, their computer simulation is time expensive. We present here some mathematical results allowing to reduce the complexity of stochastic dynamics. These methods(More)
Markov jump processes can model stochastic phenomena in molecular biology. Nevertheless , there are few mathematical results on the dynamics of these processes in their full generality. Furthermore, their computer simulation is time expensive. We present here some mathematical results allowing to reduce the complexity of stochastic dynamics. These methods(More)
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