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

Artem Logachov, Yuri Suhov, Nikita Vvedenskaya, Anatoly Yambartsev

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
JournalJournal of Applied Probability
DOIs
StateAccepted/In press - 2023

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty

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