## Studies in Probability Theory, Volume 18This collection of six articles provides the reader with a range of ideas and applications of probability theory. Written by some of leading experts in the field, the articles touch upon such topics as sequential methods in statistical inference, ergodicity and mixing for stationary random processes, distribution of maxima of independent sequences, asymptotic analysis of stochastic differential equations, mathematical aspects of statistical mechanics, and the use of entropy in the problem of isomorphism of ergodic dynamical systems. |

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### Contents

SEQUENTIAL STATISTICAL METHODS | 1 |

DEPENDENCE AND ASYMPTOTIC INDEPENDENCE | 24 |

EXTREME VALUE THEORY UNDER WEAK | 44 |

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4 other sections not shown

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apply approximation assume asymptotic Banach space Bernoulli shifts boundary bounded called consider constant continuous convergence corresponding covariance D(un defined denotes dependence determined differential diffusion discussion distribution entropy equation equivalent ergodic example exists extreme fact factor finite fixed flow follows function Gaussian give given hence holds implies independent infinite integer interest interval invariant isomorphism Lemma limit Markov process Math maximum mean measure normal observations obtain operator parameter partition positive possible probability problem procedure proof properties proved question random variables refer result satisfies sequence shown simple smooth solution space specific stationary stationary process statistical stochastic stochastic differential equations stopping sufficiently Suppose theorem theory transformation transition unit weak write zero