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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.
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Sums and Gaussian vectors, Vadim V. Jurinskij
- Language
- Released
- 1995
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- Title
- Sums and Gaussian vectors
- Language
- German
- Authors
- Vadim V. Jurinskij
- Publisher
- Springer
- Released
- 1995
- ISBN10
- 3540603115
- ISBN13
- 9783540603115
- Category
- Mathematics
- Description
- 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.