Record-breaking temperatures reveal a warming climate
We present a mathematical analysis of records drawn from independent random variables with a drifting mean. To leading order the change in the record rate is proportional to the ratio of the drift…
Record occurrence and record values in daily and monthly temperatures
We analyze the occurrence and the values of record-breaking temperatures in daily and monthly temperature observations. Our aim is to better understand and quantify the statistics of temperature…
Records in stochastic processes—theory and applications
- G. Wergen
- Environmental Science
- 26 November 2012
This review is an attempt to summarize and evaluate the progress that was made in the field of record statistics throughout the last years.
Record statistics and persistence for a random walk with a drift
- S. N. Majumdar, G. Schehr, G. Wergen
- Mathematics
- 29 June 2012
We study the statistics of records of a one-dimensional random walk of n steps, starting from the origin, and in the presence of a constant bias c. At each time step, the walker makes a random jump…
Records and sequences of records from random variables with a linear trend
We consider records and sequences of records drawn from discrete time series of the form Xn = Yn + cn, where the Yn are independent and identically distributed random variables and c is a constant…
Record statistics for biased random walks, with an application to financial data.
- G. Wergen, M. Bogner, J. Krug
- MathematicsPhysical review. E, Statistical, nonlinear, and…
- 4 March 2011
The biased random walk accounts quantitatively for the increase in the number of upper records due to the overall trend in the stock prices, and after detrending the number Of lower records in the detrended data is significantly reduced by a mechanism that remains to be identified.
Modeling record-breaking stock prices
- G. Wergen
- Economics
- 8 July 2013
Correlations of record events as a test for heavy-tailed distributions.
The method consists of converting random subsets of the data into time series with a tunable linear drift and computing the resulting record correlations to detect heavy-tailed behavior in small sets of independent random variables.
Correlations Between Record Events in Sequences of Random Variables with a Linear Trend
The statistics of records in sequences of independent, identically distributed random variables is a classic subject of study. One of the earliest results concerns the stochastic independence of…
Record statistics for multiple random walks.
- G. Wergen, S. N. Majumdar, G. Schehr
- MathematicsPhysical review. E, Statistical, nonlinear, and…
- 23 April 2012
The statistics of the number of records R(n,N) for N identical and independent symmetric discrete-time random walks of n steps in one dimension find that the mean record number grows universally as ~α(N) sqrt[n] for large n, but with a very different behavior of the amplitude α(N] for N>1 in the two cases.
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