Nonuniversal Power Law Distribution of Intensities of the Self-Excited Hawkes Process: A Field-Theoretical Approach

Kanazawa, Kiyoshi1; Sornette, Didier2,3,4

2020-09-21

10.1103/PhysRevLett.125.138301

PHYSICAL REVIEW LETTERS   影响因子和分区

0031-9007

1079-7114

The Hawkes self-excited point process provides an efficient representation of the bursty intermittent dynamics of many physical, biological, geological, and economic systems. By expressing the probability for the next event per unit time (called "intensity"), say of an earthquake, as a sum over all past events of (possibly) long-memory kernels, the Hawkes model is non-Markovian. By mapping the Hawkes model onto stochastic partial differential equations that are Markovian, we develop a field theoretical approach in terms of probability density functionals. Solving the steady-state equations, we predict a power law scaling of the probability density function of the intensities close to the critical point n = 1 of the Hawkes process, with a nonuniversal exponent, function of the background intensity nu(0) of the Hawkes intensity, the average timescale of the memory kernel and the branching ratio n. Our theoretical predictions are confirmed by numerical simulations.

SCI ; EI

英语

其他

Japan Society for the Promotion of Science KAKENHI[16K16016][20H05526]

Physics

Physics, Multidisciplinary

WOS:000571399800017

AMER PHYSICAL SOC

20204809541150

Equations of state ; Stochastic models ; Stochastic systems

Control Systems:731.1 ; Probability Theory:922.1 ; Systems Science:961

PHYSICS

Web of Science

1.Univ Tsukuba, Fac Engn Informat & Syst, Tsukuba, Ibaraki 3058573, Japan
2.Swiss Fed Inst Technol, Dept Management Technol & Econ, CH-8092 Zurich, Switzerland
3.Tokyo Inst Technol, Inst Innovat Res, Tokyo Tech World Res Hub Initiat, Tokyo 1528550, Japan
4.Southern Univ Sci & Technol SUSTech, Acad Adv Interdisciplinary Studies, Inst Risk Anal Predict & Management, Shenzhen 518055, Peoples R China

Kanazawa, Kiyoshi,Sornette, Didier. Nonuniversal Power Law Distribution of Intensities of the Self-Excited Hawkes Process: A Field-Theoretical Approach[J]. PHYSICAL REVIEW LETTERS,2020,125(13).

Kanazawa, Kiyoshi,&Sornette, Didier.(2020).Nonuniversal Power Law Distribution of Intensities of the Self-Excited Hawkes Process: A Field-Theoretical Approach.PHYSICAL REVIEW LETTERS,125(13).

Kanazawa, Kiyoshi,et al."Nonuniversal Power Law Distribution of Intensities of the Self-Excited Hawkes Process: A Field-Theoretical Approach".PHYSICAL REVIEW LETTERS 125.13(2020).