For dynamical systems, there has been much work on the statistics of
extremes. We look at the related topic of records. Namely, given a
process \(\{X_n\}\) generated by a dynamical system, we consider
record events: namely times where \(X_n>\max\{X_1,\ldots, X_{n-1}\}\).
For certain dynamical systems, we consider the distribution of times
for which records occur, and on the distribution of the corresponding
record values. This work is joint with Mike Todd.
|