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

Journal of Applied Probability. 2024. Vol. 61. No. 3. P. 781–801.

Логачёв А. В., Suhov Y., Vvedenskaya N., Yambartsev A.

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.

Ключевые слова: large deviations, birth-death processes