Level crossings and excess times due to a superposition of uncorrelated exponential pulses

A. Theodorsen and O. E. Garcia
Phys. Rev. E 97, 012110 – Published 10 January 2018

Abstract

A well-known stochastic model for intermittent fluctuations in physical systems is investigated. The model is given by a superposition of uncorrelated exponential pulses, and the degree of pulse overlap is interpreted as an intermittency parameter. Expressions for excess time statistics, that is, the rate of level crossings above a given threshold and the average time spent above the threshold, are derived from the joint distribution of the process and its derivative. Limits of both high and low intermittency are investigated and compared to previously known results. In the case of a strongly intermittent process, the distribution of times spent above threshold is obtained analytically. This expression is verified numerically, and the distribution of times above threshold is explored for other intermittency regimes. The numerical simulations compare favorably to known results for the distribution of times above the mean threshold for an Ornstein-Uhlenbeck process. This contribution generalizes the excess time statistics for the stochastic model, which find applications in a wide diversity of natural and technological systems.

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  • Received 10 April 2017

DOI:https://doi.org/10.1103/PhysRevE.97.012110

©2018 American Physical Society

Physics Subject Headings (PhySH)

Plasma PhysicsStatistical Physics & ThermodynamicsFluid DynamicsNonlinear Dynamics

Authors & Affiliations

A. Theodorsen* and O. E. Garcia

  • Department of Physics and Technology, UiT The Arctic University of Norway, N-9037 Tromsø, Norway

  • *audun.theodorsen@uit.no
  • odd.erik.garcia@uit.no

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Issue

Vol. 97, Iss. 1 — January 2018

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