## Extremes and related properties of random sequences and processes |

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assumption asymptotic distribution asymptotic independence Borel sets bounded Chapter clearly consider converges in distribution Corollary covariance function D(un defined denote density dependence disjoint intervals domain of attraction double exponential downcrossing Dr(u example extremal index Extremal Types Theorem extreme value distribution extreme value theory extreme value type F(un F(vn finite finite-dimensional distributions fixed follows at once further given gives hence holds i.i.d. sequence implies integers joint distribution Lebesgue measure lim inf lim sup limiting distribution max-stable maxima maximum mean number nondegenerate nondegenerate d.f. normalizing constants notation noted NU(I NU(T obtain P{Mn particular point process Poisson process probability proof of Theorem prove quadratic mean random variables Rayleigh distribution replaced sample paths satisfies standard normal stationary normal process stationary normal sequences stationary processes stationary sequence sufficiently large Suppose tends to zero theory u-upcrossings upcrossings write