Records in Fractal Stochastic Processes
arXiv:1704.04377 · doi:10.1063/1.4979348
Abstract
The records statistics in stationary and non-stationary fractal time series is studied extensively. By calculating various concepts in record dynamics, we find some interesting results. In stationary fractional Gaussian noises, we observe a universal behavior for the whole range of Hurst exponents. However, for non-stationary fractional Brownian motions the record dynamics is crucially dependent on the memory, which plays the role of a non-stationarity index, here. Indeed, the deviation from the results of the stationary case increases by increasing the Hurst exponent in fractional Brownian motions. We demonstrate that the memory governs the dynamics of the records as long as it causes non-stationarity in fractal stochastic processes, otherwise, it has no impact on the records statistics.
7 pages, 7 figures
References in corpus (10)
- Universal Record Statistics of Random Walks and Lévy Flights
- Record statistics for biased random walks, with an application to financial data
- Density of near-extreme events
- Record dynamics and the observed temperature plateau in the magnetic creep rate of type II superconductors
- Records in a changing world
- Finite-size scaling in extreme statistics
- Record Statistics for Multiple Random Walks
- Extreme statistics for time series: Distribution of the maximum relative to the initial value
- A record-driven growth process
- Record Statistics of Continuous Time Random Walk