Study of discrete-time Hawkes process and its compensator

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2024-06-25 DOI:10.1016/j.spl.2024.110192

Utpal Jyoti Deba Sarma, Dharmaraja Selvamuthu

引用次数: 0

Abstract

The discrete-time Hawkes process (DTHP) is a sub-class of $g$ -functions that serves as a discrete-time version of the continuous-time Hawkes process (CTHP). Like the CTHP, the DTHP also has the self-exciting property and its intensity depends on the entire history. In this paper, we study the asymptotic behavior of the DTHP and its compensator. We further analyze the moment generating function (MGF) of the DTHP and obtain some bounds and convergence results on the scaled logarithmic MGF of the DTHP.

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离散时霍克斯过程及其补偿器研究

离散时间霍克斯过程（DTHP）是 g 函数的一个子类，是连续时间霍克斯过程（CTHP）的离散时间版本。与 CTHP 一样，DTHP 也具有自激特性，其强度取决于整个历史。本文研究了 DTHP 及其补偿器的渐近行为。我们进一步分析了 DTHP 的矩生成函数 (MGF)，并得到了 DTHP 的缩放对数 MGF 的一些边界和收敛结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

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