# Records in Fractal Stochastic Processes

## TL;DR

This paper investigates record statistics in fractal stochastic processes, revealing universal behavior in stationary cases and memory-dependent dynamics in non-stationary cases, highlighting the role of non-stationarity and memory in record dynamics.

## Contribution

It provides a comprehensive analysis of record statistics in both stationary and non-stationary fractal processes, emphasizing the influence of memory and non-stationarity.

## Key findings

- Universal record behavior in stationary fractional Gaussian noises.
- Record dynamics depend on memory in non-stationary fractional Brownian motions.
- Memory influences record statistics primarily through non-stationarity.

## 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.