Graduate Texts in Mathematics Probability

Probability-2

Authors: Shiryaev, Albert N.

Free Preview
  • Along with Probability-1, forms the third English edition of the author’s classic Probability
  • Offers new problems, exercises, proofs, and applications in financial topics and mathematical statistics
  • Features a Historical Review charting the development of the mathematical theory of probability
  • Synthesizes classical ideas and results with many of the major achievements of modern probability theory
  • Suitable for a course on random processes or for independent study
see more benefits

Buy this book

eBook 55,92 €
price for Spain (gross)
  • ISBN 978-0-387-72208-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 69,67 €
price for Spain (gross)
  • ISBN 978-0-387-72207-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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.


About the authors

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.  

Video

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook 55,92 €
price for Spain (gross)
  • ISBN 978-0-387-72208-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 69,67 €
price for Spain (gross)
  • ISBN 978-0-387-72207-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Probability-2
Authors
Translated by
Chibisov, D.M.
Series Title
Graduate Texts in Mathematics
Series Volume
95
Copyright
2019
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC, part of Springer Nature
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-0-387-72208-5
DOI
10.1007/978-0-387-72208-5
Hardcover ISBN
978-0-387-72207-8
Series ISSN
0072-5285
Edition Number
3
Number of Pages
X, 348
Number of Illustrations
16 b/w illustrations
Additional Information
Originally published in one volume; English translation of the 4th original Russian edition published by © Shiryaev A. N., 2007 and © MCCME, 2007
Topics