A density dependent Markov chain (DDMC) introduced in Kurtz (1978) is a special continuous time Markov process. Examples are considered in fields like epidemics and processes which describe chemical reactions. Moreover the Yule process is a further example. In this paper we prove a moderate deviation principle for the paths of a certain class of DDMC. The proofs of the bounds utilize an exponential martingale as well as a generalized version of Girsanov’s theorem. The exponential martingale is defined according to the generator of the DDMC.

中文翻译：

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密度相关马尔可夫链的中等偏差

Kurtz (1978) 中引入的密度相关马尔可夫链 (DDMC) 是一种特殊的连续时间马尔可夫过程。在描述化学反应的流行病和过程等领域中考虑了示例。此外，Yule 过程是另一个例子。在本文中，我们证明了某类 DDMC 的路径的适度偏差原则。边界的证明利用指数鞅以及 Girsanov 定理的广义版本。指数鞅是根据 DDMC 的生成器定义的。