论文标题
反射跳槽的添加功能的大偏差
Large Deviations for Additive Functionals of Reflected Jump-Diffusions
论文作者
论文摘要
我们考虑在边界上具有反射的有界域上的跳跃扩散过程，并为其路径的一般添加剂建立长期结果。这包括其职业时间在内部和边界上的长期行为。我们得出了大偏差率函数的表征，该函数量化了过程路径的稀有事件概率的指数衰减速率。该表征依赖于具有边界约束的局部整数差异方程（PIDE）的解决方案。我们根据PIDE的数值解决方案来开发结果的实际实现。我们在一些标准示例（布朗运动，出生死亡过程）和特定的跳跃延伸模型上说明了该方法，该模型是从应用到生化反应引起的。
We consider a jump-diffusion process on a bounded domain with reflection at the boundary, and establish long-term results for a general additive process of its path. This includes the long-term behaviour of its occupation time in the interior and on the boundaries. We derive a characterization of the large deviation rate function which quantifies the rate of exponential decay of probabilities of rare events for paths of the process. The characterization relies on a solution of a partial integro-differential equation (PIDE) with boundary constraints. We develop a practical implementation of our results in terms of a numerical solution for the PIDE. We illustrate the method on a few standard examples (Brownian motion, birth-death processes) and on a particular jump-diffusion model arising from applications to biochemical reactions.
