Asymptotic results for a class of Markovian self-exciting processes

被引:0
作者
Seol, Youngsoo [1 ]
机构
[1] Dong A Univ, Dept Math, Nakdong Daero 550,37, Pusan, South Korea
关键词
Hawkes process; Inverse Markovian; Self-exciting point processes; Central limit theorems; Law of large numbers; LIMIT-THEOREMS; LARGE DEVIATIONS; HAWKES PROCESSES; MODERATE DEVIATIONS; POINT-PROCESSES; STABILITY;
D O I
10.1186/s13660-023-02989-z
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Hawkes process is a class of self-exciting point processes with clustering effect whose jump rate relies on their entire past history. This process is usually defined as a continuous-time setting and has been widely applied in several fields, including insurance, finance, queueing theory, and statistics. The Hawkes model is generally non-Markovian because the future development of a self-exciting point process is determined by the timing of past events. However, it can be Markovian in special cases such as when the exciting function is an exponential function or a sum of exponential functions. Difficulty arises when the exciting function is not an exponential function or a sum of exponentials, in which case the process can be non-Markovian. The inverse Markovian case for Hawkes processes was introduced by Seol (Stat. Probab. Lett. 155:108580, 2019) who studied some asymptotic behaviors. An extended version of the inverse Markovian Hawkes process was also studied by Seol (J. Korean Math. Soc. 58(4):819-833, 2021). In the current work, we propose a class of Markovian self-exciting processes that interpolates between the Hawkes process and the inverse Hawkes process. We derived limit theorems for the newly considered class of Markovian self-exciting processes. In particular, we established both the law of large numbers (LLN) and central limit theorems (CLT) with some key results.
引用
收藏
页数:12
相关论文
共 50 条
  • [31] The Law of Large Numbers for self-exciting correlated defaults
    Cvitanic, Jaksa
    Ma, Jin
    Zhang, Jianfeng
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2012, 122 (08) : 2781 - 2810
  • [32] Coupled Self-Exciting Process for Information Diffusion Prediction
    Liu, Yuyang
    Ma, Yuxiang
    Gao, Junruo
    Zhao, Zefang
    Li, Jun
    19TH IEEE INTERNATIONAL SYMPOSIUM ON PARALLEL AND DISTRIBUTED PROCESSING WITH APPLICATIONS (ISPA/BDCLOUD/SOCIALCOM/SUSTAINCOM 2021), 2021, : 1394 - 1401
  • [33] Portfolio liquidation games with self-exciting order flow
    Fu, Guanxing
    Horst, Ulrich
    Xia, Xiaonyu
    MATHEMATICAL FINANCE, 2022, 32 (04) : 1020 - 1065
  • [34] Modeling E-mail Networks and Inferring Leadership Using Self-Exciting Point Processes
    Fox, Eric W.
    Short, Martin B.
    Schoenberg, Frederic P.
    Coronges, Kathryn D.
    Bertozzi, Andrea L.
    JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2016, 111 (514) : 564 - 584
  • [35] Nonparametric self-exciting models for computer network traffic
    Matthew Price-Williams
    Nicholas A. Heard
    Statistics and Computing, 2020, 30 : 209 - 220
  • [36] Nonparametric self-exciting models for computer network traffic
    Price-Williams, Matthew
    Heard, Nicholas A.
    STATISTICS AND COMPUTING, 2020, 30 (02) : 209 - 220
  • [37] Self-exciting negative binomial distribution process and critical properties of intensity distribution
    Sakuraba, Kotaro
    Kurebayashi, Wataru
    Hisakado, Masato
    Mori, Shintaro
    EVOLUTIONARY AND INSTITUTIONAL ECONOMICS REVIEW, 2024, 21 (02) : 277 - 299
  • [38] Self-exciting point process models for political conflict forecasting
    Johnson, N.
    Hitchman, A.
    Phan, D.
    Smith, L.
    EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2018, 29 (04) : 685 - 707
  • [39] Branching-ratio approximation for the self-exciting Hawkes process
    Hardiman, Stephen J.
    Bouchaud, Jean-Philippe
    PHYSICAL REVIEW E, 2014, 90 (06):
  • [40] Sequential data assimilation for 1D self-exciting processes with application to urban crime data
    Santitissadeekorn, N.
    Short, M. B.
    Lloyd, D. J. B.
    COMPUTATIONAL STATISTICS & DATA ANALYSIS, 2018, 128 : 163 - 183