Asymptotic Behaviour of Linearly Transformed Sums of Random Variables (Hardcover)

V.V. Buldygin

ISBN 10: 0792346327 / ISBN 13: 9780792346326

Editore: Kluwer Academic Publishers, Dordrecht, 1997

Riguardo questo articolo

Hardcover. This text is aimed at experts in probability theory, theory of random processes and mathematcial statistics who are interested in the almost sure asymptotic behaviour in summability schemes, like operator normed sums and weighted sums. Numerous sections should be of use to those who work in Gaussian processes, stochastic recurrence equations, and probability theory in topological vector spaces. It should also be of use in university courses. 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). Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9780792346326

Dati bibliografici

• Titolo: Asymptotic Behaviour of Linearly Transformed Sums of Random Variables (Hardcover)
• Editore: Kluwer Academic Publishers, Dordrecht
• Data di pubblicazione: 1997
• Lingua: Inglese
• ISBN 10: 0792346327
• ISBN 13: 9780792346326
• Rilegatura: Hardcover
• Condizione: new

Descrizione articolo

Riassunto

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.

Recensione

`The book contains a rich amount of new material that can be of interest to many researchers. Numerous sections will be of use to researchers who work with Gaussian processes, stochastic recurrence relations, operator normed sums and weighted sums. Many topics appear in this monographic form for the first time. The excellent bibliographic list contains over 200 titles.! I strongly recommend this book to anyone interested in strong limit theorems.'
kwantitative methoden, 59 (1998)