著者

Kiyono Ken Konno Hidetoshi

出版者

American Physical Society

雑誌

Physical review E (ISSN:15393755)

巻号頁・発行日

vol.87, no.5, pp.052104, 2013-05

被引用文献数

9 3

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As a possible generalization of Beck-Cohen superstatistical processes, we study non-Gaussian processes with temporal heterogeneity of local variance. To characterize the variance heterogeneity, we define log-amplitude cumulants and log-amplitude autocovariance and derive closed-form expressions of the log-amplitude cumulants for χ2, inverse χ2, and log-normal superstatistical distributions. Furthermore, we show that χ2 and inverse χ2 superstatistics with degree 2 are closely related to an extreme value distribution, called the Gumbel distribution. In these cases, the corresponding superstatistical distributions result in the q-Gaussian distribution with q=5/3 and the bilateral exponential distribution, respectively. Thus, our finding provides a hypothesis that the asymptotic appearance of these two special distributions may be explained by a link with the asymptotic limit distributions involving extreme values. In addition, as an application of our approach, we demonstrated that non-Gaussian fluctuations observed in a stock index futures market can be well approximated by the χ2 superstatistical distribution with degree 2.

著者

Suzuki Akio Konno Hidetoshi

出版者

American Institute of Physics

雑誌

AIP Advances (ISSN:21583226)

巻号頁・発行日

vol.1, no.3, pp.032103, 2011-07

被引用文献数

9

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The dynamics of ventricular fibrillation (VF) has been studied extensively, and the initiation mechanism of VF has been elucidated to some extent. However, the stochastic dynamical nature of sustained VF remains unclear so far due to the complexity of high dimensional chaos in a heterogeneous system. In this paper, various statistical mechanical properties of sustained VF are studied numerically in 2D Beeler-Reuter-Drouhard-Roberge (BRDR) model with normal and modified ionic current conductance. The nature of sustained VF is analyzed by measuring various fluctuations of spatial phase singularity (PS) such as velocity, lifetime, the rates of birth and death. It is found that the probability density function (pdf) for lifetime of PSs is independent of system size. It is also found that the hyper-Gamma distribution serves as a universal pdf for the counting number of PSs for various system sizes and various parameters of our model tissue under VF. Further, it is demonstrated that the nonlinear Langevin equation associated with a hyper-Gamma process can mimic the pdf and temporal variation of the number of PSs in the 2D BRDR model.

著者

Konno Hidetoshi Watanabe Fumitoshi

出版者

American Institute of Physics

雑誌

Journal of Mathematical Physics (ISSN:00222488)

巻号頁・発行日

vol.48, no.10, pp.103303, 2007-10

被引用文献数

14 6

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Maximum likelihood estimator (MLE) for a generalized Cauchy process (GCP) is studied with the aid of the method of information geometry in statistics. Our GCP is described by the Langevin equation with multiplicative and additive noises. The exact expressions of MLEs are given for the two cases that the two types of noises are uncorrelated and mutually correlated. It is shown that the MLEs for these two GCPs are free from divergence even in the parameter region wherein the ordinary moments diverge. The MLE relations can be regarded as a generalized fluctuation-dissipation theorem for the present Langevin equation. Availability of them and of some other higher order statistics is demonstrated theoretically and numerically.

著者

Konno Hidetoshi

出版者

Hindawi Publishing Corporation

雑誌

Advances in mathematical physics (ISSN:16879120)

巻号頁・発行日

vol.2010, pp.504267, 2010

被引用文献数

32 3

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There are two types of master equations in describing nonequilibrium phenomena with memory effect: (i) the memory function type and (ii) the nonstationary type. A generalized Polya process is studied within the framework of a non-stationary type master equation approach. For a transition-rate with an arbitrary time-dependent relaxation function, the exact solution of a generalized Polya process is obtained. The characteristic features of temporal variation of the solution are displayed for some typical time-dependent relaxation functions reflecting memory in the systems.