CYBER DEAL: 50% off all Springer eBooks | Get this offer!

Mathematics and Its Applications

Asymptotic Behaviour of Linearly Transformed Sums of Random Variables

Authors: Buldygin, V.V., Solntsev, Serguei

Free Preview

Buy this book

eBook $89.00
price for USA in USD
  • ISBN 978-94-011-5568-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
Softcover $119.99
price for USA in USD
About this book

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.

Reviews

`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)

Table of contents (9 chapters)

Table of contents (9 chapters)
  • Random elements and their convergence (preliminary notions)

    Pages 1-46

    Buldygin, Valery (et al.)

  • Series of independent random elements

    Pages 47-121

    Buldygin, Valery (et al.)

  • Linear transformations of independent random elements and series in sequence spaces

    Pages 123-213

    Buldygin, Valery (et al.)

  • Operator-normed sums of independent random vectors

    Pages 217-268

    Buldygin, Valery (et al.)

  • Operator-normed sums of independent identically distributed random vectors

    Pages 269-306

    Buldygin, Valery (et al.)

Buy this book

eBook $89.00
price for USA in USD
  • ISBN 978-94-011-5568-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
Softcover $119.99
price for USA in USD
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Asymptotic Behaviour of Linearly Transformed Sums of Random Variables
Authors
Series Title
Mathematics and Its Applications
Series Volume
416
Copyright
1997
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-011-5568-7
DOI
10.1007/978-94-011-5568-7
Hardcover ISBN
978-0-7923-4632-6
Softcover ISBN
978-94-010-6346-3
Edition Number
1
Number of Pages
XV, 504
Additional Information
Originally published in Russian
Topics