Characterization of intermittency in renewal processes: Application to earthquakes

TL;DR

This paper introduces a new framework to characterize intermittency in renewal processes, applies it to earthquake data, and reveals dependencies in interevent times, enhancing understanding of complex temporal patterns.

Contribution

It develops a novel method linking renewal process intermittency to piecewise linear maps and applies it to earthquake data, uncovering dependencies in interevent times.

Findings

Interevent times in earthquakes are not i.i.d.

Conditional probability distributions of interevent times change systematically.

The framework provides a unified way to analyze intermittency in renewal processes.

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.