title: Stochastic nature of series of waiting times.
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.
authors.affiliation: Department of Physics, Sharif University of Technology, 11365-9161 Tehran, Iran.
authors.forename: Mehrnaz
authors.initials: M
authors.lastname: Anvari
authors.forename: Cina
authors.initials: C
authors.lastname: Aghamohammadi
authors.forename: H
authors.initials: H
authors.lastname: Dashti-Naserabadi
authors.forename: E
authors.initials: E
authors.lastname: Salehi
authors.forename: E
authors.initials: E
authors.lastname: Behjat
authors.forename: M
authors.initials: M
authors.lastname: Qorbani
authors.forename: M Khazaei
authors.initials: MK
authors.lastname: Nezhad
authors.forename: M
authors.initials: M
authors.lastname: Zirak
authors.forename: Ali
authors.initials: A
authors.lastname: Hadjihosseini
authors.forename: Joachim
authors.initials: J
authors.lastname: Peinke
authors.forename: M Reza Rahimi
authors.initials: MR
authors.lastname: Tabar