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Stochastic nature of series of waiting times

Mehrnaz Anvari1,2, Cina Aghamohammadi1, H. Dashti-Naserabadi1, E. Salehi1, E. Behjat1, M. Qorbani1, M. Khazaei Nezhad1, M. Zirak1, Ali Hadjihosseini2 et al.

Joachim Peinke2 and M. Reza Rahimi Tabar1,2

  • 1Department of Physics, Sharif University of Technology, 11365-9161 Tehran, Iran
  • 2Institute of Physics, Carl-von-Ossietzky University, 26111 Oldenburg, Germany

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Phys. Rev. E 87, 062139 – Published 28 June, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.062139

Abstract

Although fluctuations in the waiting time series have been studied for a long time, some important issues such as its long-range memory and its stochastic features in the presence of nonstationarity have so far remained unstudied. Here we find that the “waiting times” series for a given increment level have long-range correlations with Hurst exponents belonging to the interval 1/2<H<1. We also study positive-negative level asymmetry of the waiting time distribution. We find that the logarithmic difference of waiting times series has a short-range correlation, and then we study its stochastic nature using the Markovian method and determine the corresponding Kramers-Moyal coefficients. As an example, we analyze the velocity fluctuations in high Reynolds number turbulence and determine the level dependence of Markov time scales, as well as the drift and diffusion coefficients. We show that the waiting time distributions exhibit power law tails, and we were able to model the distribution with a continuous time random walk.

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Phys. Rev. E 87, 062139– Published 28 June, 2013
  • Received 7 February 2013

©2013 American Physical Society

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