Asymptotic Behaviour of Linearly Transformed Sums of Random Variables
(Sprache: Englisch)
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...
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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 randomvectors, 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.
Inhaltsverzeichnis zu „Asymptotic Behaviour of Linearly Transformed Sums of Random Variables “
Preface. Part I: Random Series and Linear Transformations of Sequences of Independent Random Elements. 1. Series of Independent Random Elements. 2. Linear Transformations of Independent Random Elements and Series in Sequence Spaces. Part II: Limit Theorems for Operator-Normed Sums of Independent Random Vectors and Their Applications. 3. Operator-Normed Sums of Independent Random Vectors and Their Applications. 4. Operator-Normed Sums of Independent Identically Distributed Random Vectors. 5. Asymptotic Properties of Gaussian Markov Sequences. 6. Continuity of Sample Paths of Gaussian Markov Processes. 7. Asymptotic Properties of Recurrent Random Sequences. 8. The Interplay Between Strong and Weak Limit Theorems for Sums of Independent Random Variables. Comments. Bibliography. Subject Index. List of Notations.
Bibliographische Angaben
- Autoren: Valery Buldygin , Serguei Solntsev
- 1997, 516 Seiten, Maße: 24 cm, Gebunden, Englisch
- Verlag: Springer Netherlands
- ISBN-10: 0792346327
- ISBN-13: 9780792346326
Sprache:
Englisch
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