Convergence of stochastic gene networks to hybrid piecewise deterministic processes

@article{Crudu2011ConvergenceOS,
  title={Convergence of stochastic gene networks to hybrid piecewise deterministic processes},
  author={Alina Crudu and A. Debussche and A. Muller and O. Radulescu},
  journal={Annals of Applied Probability},
  year={2011},
  volume={22},
  pages={1822-1859}
}
  • Alina Crudu, A. Debussche, +1 author O. Radulescu
  • Published 2011
  • Mathematics
  • Annals of Applied Probability
  • 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… CONTINUE READING
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