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Diffusion approximation of birth-death processes: Comparison in terms of large deviations and exit points

Author

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  • Pakdaman, Khashayar
  • Thieullen, Michèle
  • Wainrib, Gilles

Abstract

We compare the large deviations between jump Markov processes and their diffusion approximations for the problem of escape from a domain. It is known that the escape times are generally asymptotically different, leading to a quantitative error. In this paper we show that the escape point can also be different, which implies a qualitative error. In dimension one, for a general class of birth-and-death processes, we show that there always exists a domain [a,b] such that the jump process asymptotically escapes from a and its approximation from b.

Suggested Citation

  • Pakdaman, Khashayar & Thieullen, Michèle & Wainrib, Gilles, 2010. "Diffusion approximation of birth-death processes: Comparison in terms of large deviations and exit points," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1121-1127, July.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:13-14:p:1121-1127
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    Cited by:

    1. Giuseppe D’Onofrio & Claudio Macci & Enrica Pirozzi, 2018. "Asymptotic Results for First-Passage Times of Some Exponential Processes," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1453-1476, December.

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