Probability-2
Springer-Verlag New York Inc.
978-1-0716-1829-5 (ISBN)
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.
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.
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.
| Erscheinungsdatum | 10.06.2021 |
|---|---|
| Reihe/Serie | Graduate Texts in Mathematics ; 95 |
| Übersetzer | Dmitry M. Chibisov |
| Zusatzinfo | 16 Illustrations, black and white; X, 348 p. 16 illus. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| Schlagworte | convergence of series • Discrete time processes • Financial Engineering • Financial Mathematics • law of the iterated logarithm • markov chains • Martingales • probability textbook • Probability Theory • random processes • random processes textbook • random sequences • Stationary Random Sequences • strong law of large numbers • sums of independent random variables • Zero-one laws |
| ISBN-10 | 1-0716-1829-6 / 1071618296 |
| ISBN-13 | 978-1-0716-1829-5 / 9781071618295 |
| Zustand | Neuware |
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