来自不同来源的激励事件同时发生的多变量Hawkes过程

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Stochastic Models Pub Date : 2022-11-18 DOI:10.1080/15326349.2022.2134896

T. Bielecki, J. Jakubowski, Mariusz Niewęgłowski

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引用次数: 0

摘要

本研究对霍克斯过程理论做出了贡献。本文引入并研究了一类新的Hawkes过程，我们称之为广义Hawkes过程，以及它的特殊子类——广义多元Hawkes过程。GMHPs是多变量标记点过程，为(经典)多变量Hawkes过程家族增加了一个重要特征:它们允许对来自不同来源的同时发生的激励事件进行显式建模，即由多变量过程的不同坐标引起的。

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Multivariate Hawkes processes with simultaneous occurrence of excitation events coming from different sources

Abstract This work contributes to the theory of Hawkes processes. We introduce and study a new class of Hawkes processes that we call generalized Hawkes processes, and their special subclass – the generalized multivariate Hawkes processes (GMHPs). GMHPs are multivariate marked point processes that add an important feature to the family of the (classical) multivariate Hawkes processes: they allow for explicit modeling of simultaneous occurrence of excitation events coming from different sources, i.e., caused by different coordinates of the multivariate process.

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来源期刊

Stochastic Models 数学-统计学与概率论

CiteScore

1.30

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastic Models publishes papers discussing the theory and applications of probability as they arise in the modeling of phenomena in the natural sciences, social sciences and technology. It presents novel contributions to mathematical theory, using structural, analytical, algorithmic or experimental approaches. In an interdisciplinary context, it discusses practical applications of stochastic models to diverse areas such as biology, computer science, telecommunications modeling, inventories and dams, reliability, storage, queueing theory, mathematical finance and operations research.