Spectral theory of metastability and extinction in birth-death systems.

@article{Assaf2006SpectralTO,
  title={Spectral theory of metastability and extinction in birth-death systems.},
  author={Michael Assaf and Baruch Meerson},
  journal={Physical review letters},
  year={2006},
  volume={97 20},
  pages={200602}
}
We suggest a general spectral method for calculating the statistics of multistep birth-death processes and chemical reactions of the type mA-->nA (m and n are positive integers) which possess an absorbing state. The method employs the generating function formalism in conjunction with the Sturm-Liouville theory of linear differential operators. It yields accurate results for the extinction statistics and for the quasistationary probability distribution, including large deviations, of the… CONTINUE READING

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