The paper considers a continuous-time birth–death process where the jump rate has an asymptotically polynomial dependence on the process position. We obtain a rough exponential asymptotic for the probability of trajectories of a re-scaled process contained within a neighborhood of a given continuous nonnegative function.

中文翻译：

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非均匀生死过程的局部大偏差原理

本文考虑了一个连续时间的生死过程，该过程的跳变率与过程位置呈渐近多项式相关性。对于给定连续非负函数的邻域中包含的重新缩放过程的轨迹概率，我们获得了一个粗糙的指数渐近线。