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.
`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)
|Random series and linear transformations of sequences of independent random elements||p. 1|
|Random elements and their convergence (preliminary notions)||p. 1|
|Series of independent random elements||p. 47|
|Linear transformations of independent random elements and series in sequence spaces||p. 123|
|Limit theorems for operator-normed sums of independent random vectors and their applications||p. 215|
|Operator-normed sums of independent random vectors||p. 217|
|Operator-normed sums of independent identically distributed random vectors||p. 269|
|Asymptotic properties of Gaussian Markov sequences||p. 307|
|Continuity of sample paths of Gaussian Markov processes||p. 343|
|Asymptotic properties of recurrent random sequences||p. 363|
|The interplay between strong and weak limit theorems for sums of independent random variables||p. 417|
|Subject index||p. 487|
|List of Notations||p. 495|
|Table of Contents provided by Blackwell. All Rights Reserved.|
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER )
Number Of Pages: 504
Published: 30th June 1997
Country of Publication: NL
Dimensions (cm): 24.13 x 16.51 x 3.18
Weight (kg): 0.95