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by Serguei Solntsev,V.V. Buldygin
Download Asymptotic Behaviour of Linearly Transformed Sums of Random Variables (Mathematics and Its Applications) fb2
Mathematics
  • Author:
    Serguei Solntsev,V.V. Buldygin
  • ISBN:
    0792346327
  • ISBN13:
    978-0792346326
  • Genre:
  • Publisher:
    Springer; 1997 edition (June 30, 1997)
  • Pages:
    504 pages
  • Subcategory:
    Mathematics
  • Language:
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    1360 kb
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    1710 kb
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    1693 kb
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    4.4
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    227
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Authors: Buldygin, .

Authors: Buldygin, . 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 . evy, . a. Kolmogorov, . artman, . intner, . eller, Y. Prokhorov, and . oeve, the theory of almost sure asymptotic behaviour of increasing scalar-normed sums of independent random vari­ ables was constructed.

Series: Mathematics and Its Applications 41. As applications, the strong laws of large numbers for weighted sums of random elements and generalized summability methods are considered as applied to independent symmetric random elements

Series: Mathematics and Its Applications 416. File: PDF, 2. 4 M. As applications, the strong laws of large numbers for weighted sums of random elements and generalized summability methods are considered as applied to independent symmetric random elements. The problems we deal with in Chapters 1 and 2 as well as in the further exposition, requires invoking diverse preliminary notions whose summary is given in Chapter O. The main topic of the second part of the book is concerned with the strong limit theorems for operator-normed (matrix-normed) sums of independent random vectors in finite-dimensional Euclidean spaces (Chapters 3.

Buldygin, Serguei Solntsev Limit theorems for random sequences may conventionally be divided into .

Buldygin, Serguei Solntsev. 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).

Valery V. Buldygin, Serguei Solntsev. This book deals with the almost sure asymptotic behaviour of linearly transformed sequences of independent random variables, vectors and elements of topological vector spaces.

Asymptotic Behaviour of Linearly Transformed Sums of Random Variables. More by Valery V. Buldygin. Geometric Aspects of Probability Theory and Mathematical Statistics (MATHEMATICS AND ITS APPLICATIONS Volume 514). by Serguei Solntsev and Valery V. Metric Characterization of Random Variables and Random Processes (Translations of Mathematical Monographs). Kozachenko, Valery V.

Asymptotic Behaviour of . .has been added to your Cart. Many topics appear in this monographic form for the first time. The excellent bibliographic list contains over 200 titles.

General Note: 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

Asymptotic behaviour of linearly transformed sums of random variables. In this way the paper is quite elementary. As a further application of our method we prove stability results for sequences of independent random variables. from the Russian by V. Zaiats. re. upd. and expanded ed. Article. The law of the iterated logarithm for Gaussian sequences and its applications. A Law of the Iterated Logarithm for Double Arrays of Independent Random Variables with Applications to Regression and Time Series Models. Valery Buldygin, Serguei Solntsev. Part I: Random Series and Linear Transformations of Sequences of Independent Random Elements. 1. Series of Independent Random Elements. 2. Linear Transformations of Independent Rando. More). In this chapter, we study asymptotic properties of sample paths of random recurrent sequences (Y n, n ≥ 1) in the space of column vectors R m (m ≥ 1) which obey the infinite system of stochasti.

We aim to show you accurate product information. Manufacturers, suppliers and others provide what you see here, and we have not verified it. See our disclaimer. Asymptotic Behaviour of Linearly Transformed Sums of Random Variables. Mathematics and Its Applications (Closed).

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 sions of the strong law of large numbers and the law of the iterated logarithm. One should point out that, even in this traditional framework, there are still problems which remain open, while many definitive results have been obtained quite recently.