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An extension of Hawkes processes with ephemeral nearest effects
Stochastic Models ( IF 0.7 ) Pub Date : 2021-02-16 , DOI: 10.1080/15326349.2021.1880940
Lirong Cui 1 , Jingyuan Shen 2
Affiliation  

Abstract

Hawkes processes have been widely studied in both theory and applications because of their self-exciting effects, but there are still some questions and room left for exploring the self-exciting point processes. In this paper, an ephemeral self-exciting Hawkes process is developed, which contains 1-memory and 0-memory self-exciting point processes. After giving the definition of the ephemeral self-exciting Hawkes process, some explanations on this new point process, properties, declustering of the occurrences of events, positive and negative self-exciting effects are presented. Moments of this point process are derived as well in the paper by using the Laplace transforms and the elementary method. Some special cases are considered and the computation methods of moments are also presented by the difference method and inverse Laplace transforms, respectively. Combining dynamics of the self-exciting point process and the delayed renewal process is an important feature of the proposed ephemeral self-exciting Hawkes process, which may shed light on the related studies in the future.



中文翻译:

Hawkes过程的扩展,具有短暂的最近效应

摘要

霍克斯过程由于其自激效应而在理论和应用上都得到了广泛的研究,但是探索自激点过程仍然存在一些问题和余地。本文提出了一种短暂的自激Hawkes过程,该过程包含1个存储器和0个存储器的自激点过程。在给出了短暂的自激霍克斯过程的定义之后,对这一新的点过程,性质,事件发生的聚类,正和负自激效应作了一些解释。本文还通过使用Laplace变换和基本方法推导了这一点过程的时刻。考虑了一些特殊情况,并通过差分法和拉普拉斯逆变换提出了矩的计算方法,分别。自激点过程与延迟更新过程的动力学结合是拟议的短暂自激霍克斯过程的重要特征,这可能会为以后的相关研究提供启示。

更新日期:2021-03-24
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