## Mixing conditions and limit theorems for maxima of some stationary sequences |

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### Contents

THE LIMIT THEOREM FOR THE EARl MODEL | 10 |

SUFFICIENT CONDITIONS FOR STRONG MIXING | 25 |

Chapter Page | 35 |

3 other sections not shown

### Common terms and phrases

AR(p associative process Cauchy AR(1 characteristic function computation condition for strong defined denote dF(x dF(xn distribution function Doctor of Philosophy EAR(l example exp(l exponential extreme value theory f(xQ Gaussian processes holds implies increasing function integral Jl Jq l-pJ l-rJ Leadbetter Leadbetter's lemma lim nk lim P[M limit distribution limit theorem log2 Loynes marginal distribution Markov processes maximum n p(a n+j+1 n+j+p n+l-p n+2-p n nk nk nkx nkx order autoregressive processes order exponential P(XQ P[AQ Pj_1 positive constant probability 1-p proof quartile rates of convergence real numbers result satisfies the strong stationary processes stochastic processes strictly stationary sequence strong mixing condition sufficient condition tends to zero term contributes less uniform AR(1 unk(x Xe du dv Xe Xe Xe Xv Xn+2_p Xn+j+1=v Xn+j+p Xz/B z-Bu z-Bv z-Bv-pJ