# Records in stochastic processes—theory and applications

@article{Wergen2012RecordsIS, title={Records in stochastic processes—theory and applications}, author={Gregor Wergen}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2012}, volume={46} }

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…

## 146 Citations

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- 2013

While records and order statistics of independent and identically distributed (i.i.d.) random variables X_1, ..., X_N are fully understood, much less is known for strongly correlated random…

### The Records

- EconomicsFrank Lloyd Wright's Forgotten House
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World record setting has long attracted public interest and scientific investigation. Extremal records summarize the limits of the space explored by a process, and the historical progression of a…

### Record statistics of a strongly correlated time series: random walks and Lévy flights

- Mathematics
- 2017

We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the…

### Record Statistics of Integrated Random Walks and the Random Acceleration Process

- MathematicsJournal of Statistical Physics
- 2021

We address the theory of records for integrated random walks with finite variance. The long-time continuum limit of these walks is a non-Markov process known as the random acceleration process or the…

### Records and Occupation Time Statistics for Area-Preserving Maps

- MathematicsEntropy
- 2023

A relevant problem in dynamics is to characterize how deterministic systems may exhibit features typically associated with stochastic processes. A widely studied example is the study of (normal or…

### Records in fractal stochastic processes.

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- 2017

It is demonstrated 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 record statistics.

### Universal statistics of longest lasting records of random walks and Lévy flights

- Mathematics
- 2014

We study the record statistics of random walks after n steps, x0, x1, …, xn, with arbitrary symmetric and continuous distribution p(η) of the jumps ηi = xi − xi − 1. We consider the age of the…

### Discrete Sampling of Extreme Events Modifies Their Statistics.

- MathematicsPhysical review letters
- 2022

Extreme value (EV) statistics of correlated systems are widely investigated in many fields, spanning the spectrum from weather forecasting to earthquake prediction. Does the unavoidable discrete…

### Scaling exponent for incremental records

- Mathematics
- 2013

We investigate records in a growing sequence of identical and independently distributed random variables. The record equals the largest value in the sequence, and our focus is on the increment,…

### Persistence of random walk records

- Mathematics
- 2014

We study records generated by Brownian particles in one dimension. Specifically, we investigate an ordinary random walk and define the record as the maximal position of the walk. We compare the…

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