Records in stochastic processes -- Theory and applications

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.

42 pages, 8 figures, Published version (a few mistakes have been corrected)

References in corpus (13)

• Power-law distributions in empirical data
• Records in stochastic processes -- Theory and applications
• Universal Record Statistics of Random Walks and Lévy Flights
• Record statistics for biased random walks, with an application to financial data
• Evolution in complex systems
• Record statistics and persistence for a random walk with a drift
• Record dynamics and the observed temperature plateau in the magnetic creep rate of type II superconductors
• Records in a changing world
• Record Statistics for Multiple Random Walks
• Record Statistics of Continuous Time Random Walk
• Linear response in aging glassy systems, intermittency and the Poisson statistics of record fluctuations
• Modeling record-breaking stock prices
• Asymptotic normality for the counting process of weak records and δ-records in discrete models

Cited by in corpus (39)

• Extreme value statistics of correlated random variables: a pedagogical review
• Records in stochastic processes -- Theory and applications
• Record statistics of a strongly correlated time series: random walks and Lévy flights
• Record statistics for random walks and Lévy flights with resetting
• Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit
• Universal statistics of longest lasting records of random walks and Lévy flights
• An exactly solvable record model for rainfall
• Universal framework for record ages under restart
• Exact statistics of record increments of random walks and Lévy flights
• Record breaking bursts during the compressive failure of porous materials
• Record statistics of financial time series and geometric random walks
• Discrete Sampling of Extreme Events Modifies Their Statistics
• Modeling record-breaking stock prices
• Universal survival probability for a correlated random walk and applications to records
• Record statistics of bursts signals the onset of acceleration towards failure
• Record statistics for random walk bridges
• Statistical properties of avalanches via the c-record process
• Scaling Exponent for Incremental Records
• Distribution-free changepoint detection tests based on the breaking of records
• $\delta$-exceedance records and random adaptive walks
• Persistence of Random Walk Records
• Records for the number of distinct sites visited by a random walk on the fully-connected lattice
• Optimal protocols and the Jarzynski equality
• Record dynamics of evolving metastable systems: theory and applications
• Target finding in fibrous biological environments
• Exact solution for a sample space reducing stochastic process
• Record statistics of integrated random walks and the random acceleration process
• Time since maximum of Brownian motion and asymmetric Levy processes
• On sequences of records generated by planar random walks
• Records in Fractal Stochastic Processes
• Record statistics for a discrete-time random walk with correlated steps
• Empirical scaling of the length of the longest increasing subsequences of random walks
• Continuous Gated First-Passage Processes
• The available force in long-range interaction complex systems and its statistical physical properties
• Non-monotonic dependence of projection probabilities as a function of distinguishability
• Correspondence between noisy sample space reducing process and records in correlated random events
• Record breaking statistics near second order phase transitions
• Uncertainty in Climate Science: Not Cause for Inaction
• Records and occupation time statistics for area-preserving maps