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A large-deviation principle for birth–death processes with a linear rate of downward jumps
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Journal Article
A large-deviation principle for birth–death processes with a linear rate of downward jumps
2024
Overview
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.
Publisher
Cambridge University Press
Subject
