Given a sequence of random
variables X1, X2, ..., one is
interested in the behavior of Mn=max(X1, ...,
Xn) as n grows. Knowing this gives, for example, the
likelihood of a "catastrophic" event (i.e., an outcome whose
value exceeds a particular threshold).
For IID (Independent Identically Distributed) random variables, the limit
distribution of the (rescaled) maxima is well understood. We are interested
in the case when Xn are successive measurements of a
dynamical system (a "time series"). We show that under some
hyperbolicity assumptions, the limit behavior is the same as for IID
observations.
I will explain the IID results, and describe the methods we use in the more
general setting. The necessary Probability Theory notions will also be
explained.
This is joint work with Mark Holland (University of Exeter) and Matthew
Nicol.
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