Author | Yurinsky, Vadim Vladimirovich. author |
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Title | Sums and Gaussian Vectors [electronic resource] / by Vadim Vladimirovich Yurinsky |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1995 |

Connect to | http://dx.doi.org/10.1007/BFb0092599 |

Descript | XII, 312 p. online resource |

SUMMARY

Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject

CONTENT

Gaussian measures in euclidean space -- Seminorms of Gaussian vectors in infinite dimensions -- Inequalities for seminorms: Sums of independent random vectors -- Rough asymptotics of large deviations -- Gaussian and related approximations for distributions of sums -- Fine asymptotics of moderate deviations

Mathematics
Probabilities
Statistical physics
Dynamical systems
Mathematics
Probability Theory and Stochastic Processes
Statistical Physics Dynamical Systems and Complexity