• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.819-833
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• 2021

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history and has been widely applied in insurance, finance, queueing theory, statistics, and many other fields. Seol [27] proposed the inverse Markovian Hawkes processes and studied some asymptotic behaviors. In this paper, we consider an extended inverse Markovian Hawkes process which combines a Markovian Hawkes process and inverse Markovian Hawkes process with features of several existing models of self-exciting processes. We study the limit theorems for an extended inverse Markovian Hawkes process. In particular, we obtain a law of large number and central limit theorems.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.935-946
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• 2019

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history. We consider Hawkes processes with uniform immigrants which is a special case of the Hawkes processes with renewal immigrants. We study the limit theorems for Hawkes processes with uniform immigrants. In particular, we obtain a law of large number, a central limit theorem, and a large deviation principle.

• The Korean Journal of Applied Statistics
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• v.36 no.4
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• pp.309-322
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• 2023

The Hawkes process is a point process with self-exciting characteristics. It has been mainly used to describe seismic phenomena in which aftershocks occur due to the main earthquake. Recently, it has been used to explain various phenomena with self-exciting properties, such as the spread of infectious diseases and the spread of news on SNS. The Hawkes process can be flexibly modified according to the characteristics of events by using various types of excitation functions. Since it is difficult to implement a maximum likelihood estimator numerically, estimation methods have been improved until recently. In this paper, the conditional intensity function and excitation function are explained to describe the Hawkes process. Then, existing examples of Hawkes processes used in seismic, epidemiological, criminal, and financial fields are described and estimation methods are introduced. I analyze earthquakes that occurred in gyeongsang-do, Korea from November 2017 to December 2022, using R package ETAS.

• Proceedings of the Korea Information Processing Society Conference
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• 2019.05a
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• pp.504-507
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• 2019

모바일 광고 기술(AD Tech)분야에서 기계학습은 사용자별 CTR(Click Through Ratio) 예측[1]에 국한되어 왔으며 2016 년도부터 시행된 GDPR(General Data Protection Regulation)[2] 정책으로 인하여 AD Tech 관련 사업자의 사용자 개인정보 접근이 제한되어왔다. 그 결과 Feature Data 에 기반한 사용자 타겟팅 및 Ad Tech 산업에서 기계 학습 기술을 적용하는데 현실적 어려움을 가져왔다. 본 논문에서는 기존 연구와 현실적 한계를 극복하기 위하여 사용자가 아닌 매체별 클릭 분포를 예측하는 Hawkes Process 에 기반한 생성모델을 제안하고 그 가능성을 살펴본다.