A large-deviation principle for birth-death processes with a linear rate of downward jumps

Birth-death processes form a natural class where ideas and results on large deviations can be tested. We derive a large-deviation principle under an assumption that the rate of jump down (death) grows asymptotically linearly with the population size, while the rate of jump up (birth) grows sublinearly. We establish a large-deviation principle under various forms of scaling of the underlying process and the corresponding normalization of the logarithm of the large-deviation probabilities. The results show interesting features of dependence of the rate functional upon the parameters of the process and the forms of scaling and normalization.

Originally Published at 10.1017/jpr.2023.75

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Work Title A large-deviation principle for birth-death processes with a linear rate of downward jumps
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Open Access
Creators
  1. Artem Logachov
  2. Yuri Suhov
  3. Nikita Vvedenskaya
  4. Anatoly Yambartsev
License CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives)
Work Type Article
Publisher
  1. Journal of Applied Probability
Publication Date October 31, 2023
Publisher Identifier (DOI)
  1. https://doi.org/10.1017/jpr.2023.75
Deposited February 03, 2025

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Version 1
published

  • Created
  • Added 2112.05877v2-1.pdf
  • Added Creator Artem Logachov
  • Added Creator Yuri Suhov
  • Added Creator Nikita Vvedenskaya
  • Added Creator Anatoly Yambartsev
  • Published
  • Updated