Characterization of intermittency in renewal processes: Application to earthquakes

Abstract

We construct a one-dimensional piecewise linear intermittent map from the interevent time distribution for a given renewal process. Then, we characterize intermittency by the asymptotic behavior near the indifferent fixed point in the piecewise linear intermittent map. Thus, we provide a new framework to understand a unified characterization of intermittency, and also present the Lyapunov exponent of renewal processes. This method is applied to the occurrence of earthquakes using the Japan Meteorological Agency (JMA) catalog. We demonstrate that interevent times are not independent and identically distributed random variables by analyzing the return map of interevent times, but that there is a systematic change in conditional probability distribution functions of interevent times.

12 pages, 6 figures

References in corpus (7)

• Long-Term Clustering, Scaling, and Universality in the Temporal Occurrence of Earthquakes
• Nonergodisity of a time series obeying Lévy statistics
• The Weibull - Log Weibull Distribution for Interoccurrence Times of Earthquakes
• Generalized Arcsine Law and Stable Law in an Infinite Measure Dynamical System
• Non-Poisson dichotomous noise: higher-order correlation functions and aging
• Recurrence intervals between earthquakes strongly depend on history
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Cited by in corpus (6)

• Informational and Causal Architecture of Discrete-Time Renewal Processes
• Structure and Randomness of Continuous-Time Discrete-Event Processes
• Distributional behavior of time averages of non-$L^1$ observables in one-dimensional intermittent maps with infinite invariant measures
• Statistical Signatures of Structural Organization: The case of long memory in renewal processes
• Dynamical Instability and Transport Coefficient in Deterministic Diffusion
• Chaos suppression via adaptive feedback control of intermittency: From exactly solvable ergodic maps to interacting microbubble clusters