Ubiquitous Power Law Scaling in Nonlinear Self-Excited Hawkes Processes

Kanazawa, Kiyoshi1,2; Sornette, Didier3,4

2021-10-29

10.1103/PhysRevLett.127.188301

PHYSICAL REVIEW LETTERS   影响因子和分区

0031-9007

1079-7114

The origin(s) of the ubiquity of probability distribution functions with power law tails is still a matter of fascination and investigation in many scientific fields from linguistic, social, economic, computer sciences to essentially all natural sciences. In parallel, self-excited dynamics is a prevalent characteristic of many systems, from the physics of shot noise and intermittent processes, to seismicity, financial and social systems. Motivated by activation processes of the Arrhenius form, we bring the two threads together by introducing a general class of nonlinear self-excited point processes with fast-accelerating intensities as a function of "tension." Solving the corresponding master equations, we find that a wide class of such nonlinear Hawkes processes have the probability distribution functions of their intensities described by a power law on the condition that (i) the intensity is a fast-accelerating function of tension, (ii) the distribution of marks is two sided with nonpositive mean, and (iii) it has fast-decaying tails. In particular, Zipf's scaling is obtained in the limit where the average mark is vanishing. This unearths a novel mechanism for power laws including Zipf's law, providing a new understanding of their ubiquity.

SCI ; EI

英语

其他

JST, PRESTO Grant, Japan[JPMJPR20M2] ; Japan Society for the Promotion of Science KAKENHI[20H05526] ; National Natural Science Foundation of China[U2039202]

Physics

Physics, Multidisciplinary

WOS:000713068600005

AMER PHYSICAL SOC

20214511111686

Computational linguistics ; Nonlinear equations ; Shot noise

Computer Theory, Includes Formal Logic, Automata Theory, Switching Theory, Programming Theory:721.1 ; Probability Theory:922.1

PHYSICS

Web of Science

1.Univ Tsukuba, Fac Engn Informat & Syst, Tsukuba, Ibaraki 3058573, Japan
2.JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 3320012, Japan
3.Swiss Fed Inst Technol, Dept Management Technol & Econ, CH-8092 Zurich, Switzerland
4.Southern Univ Sci & Technol SUSTech, Acad Adv Interdisciplinary Studies, Inst Risk Anal Predict & Management Risks X, Shenzhen 518055, Peoples R China

Kanazawa, Kiyoshi,Sornette, Didier. Ubiquitous Power Law Scaling in Nonlinear Self-Excited Hawkes Processes[J]. PHYSICAL REVIEW LETTERS,2021,127(18).

Kanazawa, Kiyoshi,&Sornette, Didier.(2021).Ubiquitous Power Law Scaling in Nonlinear Self-Excited Hawkes Processes.PHYSICAL REVIEW LETTERS,127(18).

Kanazawa, Kiyoshi,et al."Ubiquitous Power Law Scaling in Nonlinear Self-Excited Hawkes Processes".PHYSICAL REVIEW LETTERS 127.18(2021).