|
Abstract
|
In this article, by using the record concept in stochastic processes, we investigate the record statistics in mono-fractal time series. For this purpose, we use the two most applicable monofractal processes in modeling various phenomena in nature, i.e., fractional Gaussian noise and fractional Brownian motion. By studying the average number of records, and, also the maximum age of records, we show that for fractional Gaussian noise, there exists a universal behavior which is independent of the correlation. In fractional Brownian motion, the maximum age of the records also is a universal quantity, but the number of records increases exponentially with Hurst index. Finally, we also investigate the size dependency of the record statistics, and demonstrate that for above-mentioned quantities, a power-law behavior exists.
|