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Titlebook: Asymptotic Behaviour of Linearly Transformed Sums of Random Variables; Valery Buldygin,Serguei Solntsev Book 1997 Springer Science+Busines

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发表于 2025-3-21 16:53:21 | 显示全部楼层 |阅读模式
期刊全称Asymptotic Behaviour of Linearly Transformed Sums of Random Variables
影响因子2023Valery Buldygin,Serguei Solntsev
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学科分类Mathematics and Its Applications
图书封面Titlebook: Asymptotic Behaviour of Linearly Transformed Sums of Random Variables;  Valery Buldygin,Serguei Solntsev Book 1997 Springer Science+Busines
影响因子Limit theorems for random sequences may conventionally be divided into two large parts, one of them dealing with convergence of distributions (weak limit theorems) and the other, with almost sure convergence, that is to say, with asymptotic prop­ erties of almost all sample paths of the sequences involved (strong limit theorems). Although either of these directions is closely related to another one, each of them has its own range of specific problems, as well as the own methodology for solving the underlying problems. This book is devoted to the second of the above mentioned lines, which means that we study asymptotic behaviour of almost all sample paths of linearly transformed sums of independent random variables, vectors, and elements taking values in topological vector spaces. In the classical works of P.Levy, A.Ya.Khintchine, A.N.Kolmogorov, P.Hartman, A.Wintner, W.Feller, Yu.V.Prokhorov, and M.Loeve, the theory of almost sure asymptotic behaviour of increasing scalar-normed sums of independent random vari­ ables was constructed. This theory not only provides conditions of the almost sure convergence of series of independent random variables, but also studies different ver­ sio
Pindex Book 1997
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发表于 2025-3-21 20:58:41 | 显示全部楼层
Operator-normed sums of independent identically distributed random vectorserms have infinite second moments, the equivalence of scalar and operator normalizations may fail to hold. In Section 4.4, a complete description of those distributions of identically distributed symmetric summands is given, whose sums obey the iterated logarithm type law under appropriate operator normalizations.
发表于 2025-3-22 00:41:14 | 显示全部楼层
Shan-Hwei Nienhuys-Cheng,Roland Wolferplay enables extending some statements of Chapter 1 to the linear transformations of sequences of independent random elements and, in particular, establishing the contraction principles, the Gaussian majorization principle, etc.
发表于 2025-3-22 06:25:09 | 显示全部楼层
Lecture Notes in Computer ScienceThe result reads as follows: In order for a sequence of constants (., . ≥ 1) to exist and obey the properties and it is necessary and sufficient that the common distribution function .(.) lie in the domain of partial attraction of the normal law. Observe that the latter condition is equivalent to the equality
发表于 2025-3-22 12:14:10 | 显示全部楼层
Linear transformations of independent random elements and series in sequence spaceserplay enables extending some statements of Chapter 1 to the linear transformations of sequences of independent random elements and, in particular, establishing the contraction principles, the Gaussian majorization principle, etc.
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Operator-normed sums of independent random vectors recently when studying operator normalizations (especially in the framework of almost sure convergence) began, though these normalizations are more adequate for reflecting the asymptotic behaviour of sums of independent random vectors.
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