Generalization of the Beck-Cohen superstatistics

Sob’yanin, D. N.

doi:10.1103/physreve.84.051128

Cited by 15 publications

(3 citation statements)

References 62 publications

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“…The q -exponential scaling behavior of interevent times for T < T c can be originated from a simple mechanism, namely a gamma-distributed allocated parameter ( β ) of the local Poisson process, and may be used to explain the interevent time distribution in aftershock sequences. The T c value indicated that in the early aftershock period the majority of interevent times had T values lower than T c and their distributions were described by NESP, while properties such as long-range memory, associated with NESP, became less prominent as the system relaxed and the BG statistical physics recovered [ 56 , 57 , 58 , 59 , 60 , 61 ].…”

Section: Discussionmentioning

confidence: 99%

“…The q -exponential behavior of the interevent times can further be viewed in terms of superstatistics, which are based on a superposition of ordinary local equilibrium statistical mechanics with a suitable intensive parameter ( β ) that varies as a gamma distribution on a reasonably wide temporal scale and is supplementary to NESP [ 19 , 23 , 61 , 62 , 63 , 64 , 65 ].…”

Section: Discussionmentioning

confidence: 99%

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Universal Non-Extensive Statistical Physics Temporal Pattern of Major Subduction Zone Aftershock Sequences

Anyfadi

Avgerinou

Michas

et al. 2022

Entropy

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Large subduction-zone earthquakes generate long-lasting and wide-spread aftershock sequences. The physical and statistical patterns of these aftershock sequences are of considerable importance for better understanding earthquake dynamics and for seismic hazard assessments and earthquake risk mitigation. In this work, we analyzed the statistical properties of 42 aftershock sequences in terms of their temporal evolution. These aftershock sequences followed recent large subduction-zone earthquakes of M ≥ 7.0 with focal depths less than 70 km that have occurred worldwide since 1976. Their temporal properties were analyzed by investigating the probability distribution of the interevent times between successive aftershocks in terms of non-extensive statistical physics (NESP). We demonstrate the presence of a crossover behavior from power-law (q ≠ 1) to exponential (q = 1) scaling for greater interevent times. The estimated entropic q-values characterizing the observed distributions range from 1.67 to 1.83. The q-exponential behavior, along with the crossover behavior observed for greater interevent times, are further discussed in terms of superstatistics and in view of a stochastic mechanism with memory effects, which could generate the observed scaling patterns of the interevent time evolution in earthquake aftershock sequences.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Universal Non-Extensive Statistical Physics Temporal Pattern of Major Subduction Zone Aftershock Sequences

Anyfadi

Avgerinou

Michas

et al. 2022

Entropy

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“…The actual value of the signal x may be random variable with the distribution depending on the parameters and, consequently, on the slowly varying averagex. In such superstatistical approach [4,59,1,24,5,64,55,65] the distribution P (x) of the signal x is a superposition of the conditional distribution ϕ(x|x) and the local stationary distribution p(x) of the parameterx,…”

Section: Superstatistical Frameworkmentioning

confidence: 99%

Nonextensive Statistical Mechanics Distributions and Dynamics of Financial Observables From the Nonlinear Stochastic Differential Equations

Ruseckas

Gontis

Kaulakys

2012

Advs. Complex Syst.

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We present nonlinear stochastic differential equations, generating processes with the q-exponential and q-Gaussian distributions of the observables, i.e. with the long-range power-law autocorrelations and 1/f β power spectral density. Similarly, the Tsallis q-distributions may be obtained in the superstatistical framework as a superposition of different local dynamics at different time intervals. In such approach, the average of the stochastic variable is generated by the nonlinear stochastic process, while the local distribution of the signal is exponential or Gaussian one, conditioned by the slow average. Further we analyze relevance of the generalized and adapted equations for modeling the financial processes. We model the inter-trade durations, the trading activity and the normalized return using the superstatistical approaches with the exponential and normal distributions of the local signals driven by the nonlinear stochastic process.Many complex systems show large fluctuations that follow non-Gaussian, heavytailed distributions with the power-law temporal correlations, scaling and the fractal features [42,44,41]. These distributions, scaling, self-similarity and fractality are often related with the Tsallis nonextensive statistical mechanics [60,48,61,62,57] and with 1/f β noise (see, e.g. [41,30,29,14,37,54], and references herein). Often nonextensive statistical mechanics represents a consistent theoretical background for the investigation of complex systems, [61,62,57]. On the other hand, a usual way to describe stochastic evolution and the properties of complex systems is by the stochastic differential equations (SDE) [16,52,13,64,65]. Such nondeterministic equations of motion are used for modeling the financial systems, as well [38,44,27,20,19,21,22].There are empirically established facts that the trading activity, trading volume, and volatility are stochastic variables with the long-range correlation [10,46,15]. However, these aspects are not accounted for in some widely used models of the financial systems. Moreover, the trading volume and the trading activity are positively correlated with the market volatility, while the trading volume and volatility show the same type of the long memory behavior [40], including 1/f β noise [21,22].The purpose of this article is to model the inter-trade durations, the trading activity and the normalized return using the superstatistical approaches with the exponential and normal distributions of the local signals driven by the nonlinear stochastic process. We present a class of nonlinear stochastic differential equations giving the power-law behavior of the probability density function (PDF) of the signal intensity and of the power spectral density (1/f β noise) in any desirably wide range of frequency. Modifications of these equations by introducing an additional parameter yields Tsallis distributions preserving 1/f β behavior of the power spectral density. The superstatistical framework [4,59,1,2,63,24,5] using a fast dynamics with the slowly changing parameter...

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Environmental superstatistics

Yalçın

Beck

2013

Physica A: Statistical Mechanics and its Applications

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Generalization of the Beck-Cohen superstatistics

Cited by 15 publications

References 62 publications

Universal Non-Extensive Statistical Physics Temporal Pattern of Major Subduction Zone Aftershock Sequences

Universal Non-Extensive Statistical Physics Temporal Pattern of Major Subduction Zone Aftershock Sequences

Nonextensive Statistical Mechanics Distributions and Dynamics of Financial Observables From the Nonlinear Stochastic Differential Equations

Environmental superstatistics

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