Mathematics of Probability

Inbunden, Engelska, 2013

Del i serien Graduate Studies in Mathematics

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Beskrivning

This book covers the basics of modern probability theory. It begins with probability theory on finite and countable sample spaces and then passes from there to a concise course on measure theory, which is followed by some initial applications to probability theory, including independence and conditional expectations. The second half of the book deals with Gaussian random variables, with Markov chains, with a few continuous parameter processes, including Brownian motion, and, finally, with martingales, both discrete and continuous parameter ones. The book is a self-contained introduction to probability theory and the measure theory required to study it.

Produktinformation

Utgivningsdatum:2013-08-30
Vikt:680 g
Format:Inbunden
Språk:Engelska
Serie:Graduate Studies in Mathematics
Antal sidor:284
Förlag:American Mathematical Society
ISBN:9781470409074

Utforska kategorier

Matematisk statistik inom Naturvetenskap och teknik

Mer om författaren

Daniel W. Stroock, Massachusetts Institute of Technology, Cambridge, MA, USA

Recensioner i media

... I regard this book highly, and I recommend it for course use as well as for independent study." - MAA Reviews"This book is a very thorough advanced undergraduate/beginning graduate course on probability theory for students who have a good background in modern mathematical ideas. ... [W]hat distinguishes this book from its many competitors is the thoroughness of argument, and the tasteful choice of auxiliary topics that complement the main menu. ... The book is replete with carefully chosen exercise for readers to test their understanding. Another nice touch is that the author always takes care to let the reader know who originally came up with a particularly clever argument or method. In this way, readers get a healthy exposure to ways of thinking originating from Doeblin, Doob, Dynkin, Huygens, Kac, Kolmogorov, Livy, Marcinkiewicz and Wiener, among many others. This is a very good book on which to base a graduate course or to use for self-study." - David Applebaum, University of Sheffield, South Yorkshire, UK"Mathematics of Probability is a very enjoyable book. It is definitely a book for graduate students, but it manages to begin exploring the subject without a lot of prerequisites. ... It manages to discuss rigorously, and in a mostly self-contained manner, advanced topics which are not found in undergraduate books. ... It is a good book for independent study. It does not overwhelm the reader with exercises (each section ends with several problems). The footnotes and the comments at the end of each chapter are to the point and help the reader keep focus. ... All in all, I regard this book highly and I recommend it for course use as well as for independent study." - Florin Catrina, MAA Reviews

Innehållsförteckning

PrefaceSome background and preliminariesProbability theory on uncountable sample spacesSome applications to probability theoryThe central limit theorem and Gaussian distributionsDiscrete parameter stochastic processesSome continuous-time processesMartingalesNotationBibliographyIndex