## Asymptotic Methods in the Theory of Gaussian Processes and Fieldsdoes not need NBB copy |

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### Contents

The Method of Comparison | 37 |

The Double Sum Method | 97 |

The Methods of Moments | 143 |

Limit Theorems for the Number of High Excursions and | 169 |

203 | |

### Other editions - View all

Asymptotic Methods in the Theory of Gaussian Processes and Fields Vladimir I. Piterbarg Limited preview - 2012 |

Asymptotic Methods in the Theory of Gaussian Processes and Fields Vladimir I. Piterbarg No preview available - 2012 |

### Common terms and phrases

arbitrary assertion assume asymptotic behavior central limit theorem condition of strong conditional expectation conditions of Lemma consider convergence theorem Corollary corresponding covariance function covariance function r(t covariance matrix cube differentiable discretizing distribution density dominated convergence theorem double sum equal estimate exact asymptotic exists a constant exists a number field with zero field X(t finite finite-dimensional distributions Gaussian field Gaussian homogeneous field Gaussian process Gaussian random field Gaussian stationary process Gaussian vectors high excursions holds independent integral Introduction Let X(t limsup max X(t maximum mean squared sense method Minkowski functionals monotone non-degenerate obtain one-dimensional P(max Y(t parameter set partition Pickands polynomials process with zero process X(t processes and fields random variables rectangles right-hand side satisfying the conditions segment sequence Slepian inequality stationary process stochastic processes strong mixing summand Suppose Taylor formula tends to zero Theorem 7.1 uniformly unit variance zero mean