Bounds for the expected value of one-step processes

@article{Armbruster2015BoundsFT,
  title={Bounds for the expected value of one-step processes},
  author={Benjamin Armbruster and {\'A}d{\'a}m Besenyei and P{\'e}ter L. Simon},
  journal={ArXiv},
  year={2015},
  volume={abs/1505.00898}
}
Mean-field models are often used to approximate Markov processes with large state-spaces. One-step processes, also known as birth-death processes, are an important class of such processes and are processes with state space $\{0,1,\ldots,N\}$ and where each transition is of size one. We derive explicit bounds on the expected value of such a process, bracketing it between the mean-field model and another simple ODE. Our bounds require that the Markov transition rates are density dependent… 

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