Construction of Ito model for Geoelectrical Signals

TL;DR

This paper develops an Ito stochastic differential equation model to describe geoelectrical signals in seismic areas, demonstrating its effectiveness especially on less variable data segments, and suggesting these signals approximate a Markov diffusion process.

Contribution

It presents a method to construct an Ito model for geoelectrical signals, highlighting its suitability for modeling seismic area data and its better performance on low-variability segments.

Findings

Ito model fits well to the entire time series

Model performs better on low-variability data fragments

Detrended signals approximate Markov diffusion processes

Abstract

Ito stochastic differential equation governs one-dimensional diffusive Markov process. Geoelectrical signals measured in seismic areas can be considered as the result of competitive and collective interactions among system elements. The Ito equation may constitute a good macroscopic model of such phenomenon in which microscopic interactions are adequately averaged. The present study shows how to construct Ito model for a geoelectrical time series measured in a seismic area of southern Italy. Our results reveal that Ito model describes quite well the whole time series, but performs better when one considers fragments of the data set with lower variability range (absent or rare large fluctuations) . Our findings show that generally detrended geoelectrical time series can be considered as an approximation of the Markov diffusion process.