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 language | English (US) |
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Pages (from-to) | 781-801 |
Number of pages | 21 |
Journal | Journal of Applied Probability |
Volume | 61 |
Issue number | 3 |
DOIs | |
State | Published - Sep 1 2024 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- General Mathematics
- Statistics, Probability and Uncertainty