具有随机强度计数过程的Kalikow分解及其在模拟算法中的应用
Kalikow decomposition for counting processes with stochastic intensity and application to simulation algorithms
摘要：
我们提出了一个新的Kalikow分解的连续时间多元计数过程，潜在的无限网络。我们证明了存在这样的分解在各种情况下。这种分解使我们能够推导出模拟算法，该算法适用于具有潜在无限网络但强度有界的平稳过程，或者适用于有限网络中强度无界且0之前为空的过程。Kalikow分解是不唯一的，我们讨论了在某些情况下的算法效率方面的分解的选择。我们应用这些方法的几个例子：线性霍克斯过程，年龄相关的霍克斯过程，指数霍克斯过程，Galves-Löcherbach过程。
英文摘要：
We propose a new Kalikow decomposition for continuous time multivariate counting processes, on potentially infinite networks. We prove the existence of such a decomposition in various cases. This decomposition allows us to derive simulation algorithms that hold either for stationary processes with potentially infinite network but bounded intensities, or for processes with unbounded intensities in a finite network and with empty past before 0. The Kalikow decomposition is not unique and we discuss the choice of the decomposition in terms of algorithmic efficiency in certain cases. We apply these methods on several examples: linear Hawkes process, age dependent Hawkes process, exponential Hawkes process, Galves-Löcherbach process.
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