Records in stochastic processes -- Theory and applications

TL;DR

This paper reviews recent advances in the theory and applications of record statistics in stochastic processes, covering uncorrelated and correlated cases across various fields like climate, sports, and finance.

Contribution

It provides a comprehensive summary of recent progress in record statistics, highlighting new theoretical insights and diverse applications in real-world data analysis.

Findings

Record statistics of uncorrelated variables have been extensively studied.

Applications include modeling temperature records and their link to global warming.

Recent progress includes understanding record behavior in correlated processes like random walks.

Abstract

In recent years there has been a surge of interest in the statistics of record-breaking events in stochastic processes. Along with that, many new and interesting applications of the theory of records were discovered and explored. The record statistics of uncorrelated random variables sampled from time-dependent distributions was studied extensively. The findings were applied in various areas to model and explain record-breaking events in observational data. Particularly interesting and fruitful was the study of record-breaking temperatures and their connection with global warming, but also records in sports, biology and some areas in physics were considered in the last years. Similarly, researchers have recently started to understand the record statistics of correlated processes such as random walks, which can be helpful to model record events in financial time series. This review is an attempt to summarize and evaluate the progress that was made in the field of record statistics throughout the last years.