## Dependence in Probability and StatisticsPaul Doukhan, Gabriel Lang, Donatas Surgailis, Gilles Teyssière This account of recent works on weakly dependent, long memory and multifractal processes introduces new dependence measures for studying complex stochastic systems and includes other topics such as the dependence structure of max-stable processes. |

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### Contents

Permutation and bootstrap statistics underinfinite variance | 1 |

Representations Ergodic Properties and Statistical Applications | 21 |

Best attainable rates of convergence for the estimation of the memory parameter | 43 |

Harmonic analysis tools for statistical inference in the spectral domain | 59 |

On the impact of the number of vanishing moments on the dependence structures of compound Poisson motion and fractional Brownian motion in ... | 71 |

Multifractal scenarios for products of geometric OrnsteinUhlenbeck type processes | 103 |

A new look at measuring dependence | 123 |

Robust regression with infinite moving average errors | 143 |

A note on the monitoring of changes in linear models with dependent errors | 159 |

Testing for homogeneity of variance in the wavelet domain | 175 |

Lecture Notes in Statistics | 206 |

### Common terms and phrases

analysis Applications assume asymptotic Barndorff-Nielsen bootstrap bounded Brownian bridge central limit theorem change point consider Corollary correlation functions covariance function CUSUM defined denote dependence measures dependence structure Doukhan e-mail empirical ergodic exponents extremal index finite fractional Brownian motion Hence Horváth implies independent inequality infinitely divisible infinitely divisible cascades kernels Lemma Leonenko Lévy processes limit distribution linear long memory long-range dependence matrix matroid max–stable processes memory parameter multivariate nondecreasing Notes in Statistics number of vanishing O-Fréchet Observe obtained Ornstein-Uhlenbeck partial sums permutation procedure proof of Theorem properties Proposition quantile random variables rate of convergence regression regularly varying satisfies scale scalogram second order Section sequence Shieh simulations spectral density spectral functions stationary process stochastic processes Taqqu tempered stable Theorem 3.1 theory tion values vanishing moments vector wavelet coefficients Wiener process