Albert N. Shiryaev

Probability-2 (eBook, PDF)

Übersetzer: Chibisov, Dmitry M.

• Format: PDF

Produktbeschreibung

This textbook is the second volume of a pair that presents the latest English edition of the author's classic, Probability. Building on the foundations established in the preceding Probability-1, this volume guides the reader on to the theory of random processes. The new edition includes expanded material on financial mathematics and financial engineering; new problems, exercises, and proofs throughout; and a Historical Review charting the development of the mathematical theory of probability. Suitable for an advanced undergraduate or beginning graduate student with a course in probability theory, this volume forms the natural sequel to Probability-1.

Probability-2 opens with classical results related to sequences and sums of independent random variables, such as the zero-one laws, convergence of series, strong law of large numbers, and the law of the iterated logarithm. The subsequent chapters go on to develop the theory of random processes with discrete time: stationary processes, martingales, and Markov processes. The Historical Review illustrates the growth from intuitive notions of randomness in history through to modern day probability theory and theory of random processes.

Along with its companion volume, this textbook presents 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 throughout.

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Produktdetails

• Verlag: Springer-Verlag GmbH
• Seitenzahl: 348
• Erscheinungstermin: 23. März 2019
• Englisch
• ISBN-13: 9780387722085
• Artikelnr.: 55849931

Autorenporträt

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 recipient of the A.N. Kolmogorov Prize of the Russian Academy of Sciences in 1994 and the A.A. Markov Prize in 1974. His numerous other titles include Problems in Probability, translated by A. Lyasoff, which offers more than 1500 exercises and problems as a supplement to Probability.

Translator 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 and is the translator of over 6 volumes from Russian to English.

Inhaltsangabe

Preface.- Chapter 4: Sequences and Sums of Independent Random Variables.- Chapter 5: Stationary (Strict Sense) Random Sequences and Ergodic Theory.- Chapter 6: Stationary (Wide Sense) Random Sequences: L2-Theory.- Chapter 7: Martingales.- Chapter 8: Markov Chains.- Historical of Bibliographical Notes (Chapters 4-8).- References.- Index.- Index of Symbols.

Rezensionen

About the First English Edition:

"It is clear that this book contains important and interesting results obtained through a long time period, beginning with the classical Bernoulli's law of large numbers, and ending with very recent results concerning convergence of martingales and absolute continuity of probability measures. Let us note especially that the great number of ideas, notions and statements in the book are well-motivated, explained in detail and illustrated by suitably chosen examples and a large number of exercises. Thus, the present book is a synthesis of all significant classical ideas and results, and many of the major achievements of modern probability theory. In the whole it is a welcome addition to mathematical literature and can become an indispensable textbook for courses in stochastics." -- J. Stoyanov, Zentralblatt

"I think this would be an excellent text by itself for an advanced course in probability." (Allen Stenger, MAA Reviews, October 26, 2019)