Abstract

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.

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