Sums and Gaussian Vectors
Yurinsky, Vadim Vladimirovich.
Sums and Gaussian Vectors [electronic resource] / by Vadim Vladimirovich Yurinsky. - XII, 312 p. online resource. - Lecture Notes in Mathematics, 1617 0075-8434 ; . - Lecture Notes in Mathematics, 1617 .
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.
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.
9783540447917
10.1007/BFb0092599 doi
Distribution (Probability theory.
Statistical physics.
Probability Theory and Stochastic Processes.
Complex Systems.
Statistical Physics and Dynamical Systems.
QA273.A1-274.9 QA274-274.9
519.2
Sums and Gaussian Vectors [electronic resource] / by Vadim Vladimirovich Yurinsky. - XII, 312 p. online resource. - Lecture Notes in Mathematics, 1617 0075-8434 ; . - Lecture Notes in Mathematics, 1617 .
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.
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.
9783540447917
10.1007/BFb0092599 doi
Distribution (Probability theory.
Statistical physics.
Probability Theory and Stochastic Processes.
Complex Systems.
Statistical Physics and Dynamical Systems.
QA273.A1-274.9 QA274-274.9
519.2