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Journal Article

Example of a Non-standard Extreme Value Law

Haydn N., Kupsa Michal

: Ergodic Theory and Dynamical Systems vol.35, 6 (2015), p. 1902-1912

: extreme-value law, rotations of unit circle, non-mixing systems, discrete law, Gumbel distribution, Weibull distribution, Frechet distribution, return times

: 10.1017/etds.2014.11

: http://library.utia.cas.cz/separaty/2014/SI/kupsa-0434480.pdf

(eng): It has been shown that sufficiently well mixing dynamical systems with positive entropy have extreme-value laws which in the limit converge to one of the three standard distributions known for independently and identically distributed processes, namely Gumbel, Fréchet and Weibull distributions. In this short note, we give an example which has a non-standard limiting distribution for its extreme values. Rotations of the circle by irrational numbers are used and it will be shown that the limiting distribution is a step function where the limit has to be taken along a suitable sequence given by the convergents.

: BB

07.01.2019 - 08:39