Probability-1

Albert N. Shiryaev (Autor)

Buch | Hardcover

486 Seiten

2016 | 3rd ed. 2016
Springer-Verlag New York Inc.
978-0-387-72205-4 (ISBN)

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This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, the measure-theoretic foundations of probability theory, weak convergence of probability measures, and the central limit theorem. Many examples are discussed in detail, and there are a large number of exercises. The book is accessible to advanced undergraduates and can be used as a text for independent study.

To accommodate the greatly expanded material in the third edition of Probability, the book is now divided into two volumes. This first volume contains updated references and substantial revisions of the first three chapters of the second edition. In particular, new material has been added on generating functions, the inclusion-exclusion principle, theorems on monotonic classes (relying on a detailed treatment of “π-λ” systems), and the fundamental theorems of mathematical statistics.

Albert N. Shiryaev is Chief Scientific Researcher and Professor of Probability Theory and Mathematical Statistics at the Steklov Mathematical Institute of the Russian Academy of Sciences and Head of the Department of Probability Theory in the Mechanics and Mathematics Faculty at Lomonosov Moscow State University. He is the author of several books, including Problems in Probability [translated by Andrew Lyasov], Optimal Stopping Rules [translated by A.B. Aries], and Statistics of Random Processes [with Robert S. Liptser]. He was the recipient of the A.N. Kolmogorov Prize of the Russian Academy of Sciences in 1994 and the A.A. Markov Prize in 1974. Dmitry M. Chibisov is Leading Scientific Researcher and Professor of Probability Theory and Mathematical Statistics at the Steklov Mathematical Institute of the Russian Academy of Sciences. He is the Editor-in-Chief of the journal Mathematical Methods of Statistics.

Introduction.- Elementary Probability Theory.- Mathematical Foundations of Probability Theory.- Convergence of Probability Measures. Central Limit Theorem.

Erscheint lt. Verlag	9.7.2016
Reihe/Serie	Graduate Texts in Mathematics ; 95
Übersetzer	Dmitry M. Chibisov
Zusatzinfo	39 Illustrations, black and white; XVII, 486 p. 39 illus.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	0-387-72205-X / 038772205X
ISBN-13	978-0-387-72205-4 / 9780387722054
Zustand	Neuware