Malempati M. Rao – författare
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This book is a revised and expanded edition of a successful graduate and reference text. The material in the book is designed for a standard graduate course on probability theory, including some important applications. This new edition contains a detailed treatment of the core area of probability, and both structural and limit results are presented in full detail. Compared to the first edition, the material and presentation are better highlighted with several (small and large) alterations made to each chapter. Key features of the book include:
- Indicating the need for abstract theory even in applications and showing the inadequacy of existing results for certain apparently simple real-world problems
- Attempting to deal with the existence problems for various classes of random families that figure in the main results of the subject
- Providing a treatment of conditional expectations and of conditional probabilities that is more complete than in other existing textbooks
Since this is a textbook, essentially all proofs are given in complete detail (even at the risk of repetition), and some key results are given multiple proofs when each argument has something to contribute.
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This is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander''s fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics.
The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.
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