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 Arnaud Debussche and A. Muller and Ovidiu Radulescu},
  journal={Annals of Applied Probability},
  year={2011},
  volume={22},
  pages={1822-1859}
}
  • Alina Crudu, Arnaud Debussche, +1 author Ovidiu 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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