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Asymptotic Behaviour Of Linearly Transformed Sums Of Random Variables
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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 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. Books, Science and Geography~~Mathematics~~Applied Mathematics, Asymptotic Behaviour Of Linearly Transformed Sums Of Random Variables~~Book~~9780792346326~~Serguei Solntsev, Valery Buldygin, , , , , , , , , ,, [PU: Kluwer Academic Publishers]

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Asymptotic Behaviour of Linearly Transformed Sums of Random Variables: Hardback: Kluwer Academic Publishers: 9780792346326: 01 Jun 1997: Deals with the almost sure asymptotic behaviour of linearly transformed sequences of independent random variables, vectors and elements of topological vector spaces. This book is intended for experts in probability theory and theory of random processes. 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. Probability & Statistics, , , , Asymptotic Behaviour of Linearly Transformed Sums of Random Variables, Valery Buldygin, 9780792346326, Kluwer Academic Publishers, , , , ,, [PU: Kluwer Academic Publishers]

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[EAN: 9780792346326], Neubuch, [PU: Springer Netherlands Jun 1997], ZUFALL (STATISTIK), - This book deals with the almost sure asymptotic behaviour of linearly transformed sequences of independent random variables, vectors and elements of topological vector spaces. The main subjects dealing with series of independent random elements on topological vector spaces, and in particular, in sequence spaces, as well as with generalized summability methods which are treated here are strong limit theorems for operator-normed (matrix normed) sums of independent finite-dimensional random vectors and their applications; almost sure asymptotic behaviour of realizations of one-dimensional and multi-dimensional Gaussian Markov sequences; various conditions providing almost sure continuity of sample paths of Gaussian Markov processes; and almost sure asymptotic behaviour of solutions of one-dimensional and multi-dimensional stochastic recurrence equations of special interest. §Many topics, especially those related to strong limit theorems for operator-normed sums of independent random vectors, appear in monographic literature for the first time. §Audience: The book is aimed at experts in probability theory, theory of random processes and mathematical statistics who are interested in the almost sure asymptotic behaviour in summability schemes, like operator normed sums and weighted sums, etc. Numerous sections will be of use to those who work in Gaussian processes, stochastic recurrence equations, and probability theory in topological vector spaces. As the exposition of the material is consistent and self-contained it can also be recommended as a textbook for university courses. 516 pp. Englisch

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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. mathematics,physics,science and math,science and math,statistics,system theory,textbooks Statistics, Springer

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Asymptotic Behaviour of Linearly Transformed Sums of Random Variables
Autor:

Solntsev, Serguei; Buldygin, V. V.

Titel:

Asymptotic Behaviour of Linearly Transformed Sums of Random Variables

ISBN-Nummer:

This book deals with the almost sure asymptotic behaviour of linearly transformed sequences of independent random variables, vectors and elements of topological vector spaces. The main subjects dealing with series of independent random elements on topological vector spaces, and in particular, in sequence spaces, as well as with generalized summability methods which are treated here are strong limit theorems for operator-normed (matrix normed) sums of independent finite-dimensional random vectors and their applications; almost sure asymptotic behaviour of realizations of one-dimensional and multi-dimensional Gaussian Markov sequences; various conditions providing almost sure continuity of sample paths of Gaussian Markov processes; and almost sure asymptotic behaviour of solutions of one-dimensional and multi-dimensional stochastic recurrence equations of special interest. Many topics, especially those related to strong limit theorems for operator-normed sums of independent random vectors, appear in monographic literature for the first time. Audience: The book is aimed at experts in probability theory, theory of random processes and mathematical statistics who are interested in the almost sure asymptotic behaviour in summability schemes, like operator normed sums and weighted sums, etc. Numerous sections will be of use to those who work in Gaussian processes, stochastic recurrence equations, and probability theory in topological vector spaces. As the exposition of the material is consistent and self-contained it can also be recommended as a textbook for university courses.

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EAN (ISBN-13): 9780792346326
ISBN (ISBN-10): 0792346327
Gebundene Ausgabe
Erscheinungsjahr: 1997
Herausgeber: Springer-Verlag GmbH
524 Seiten
Gewicht: 0,941 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 02.03.2008 07:07:22
Buch zuletzt gefunden am 26.12.2016 14:23:03
ISBN/EAN: 9780792346326

ISBN - alternative Schreibweisen:
0-7923-4632-7, 978-0-7923-4632-6


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