A Basic Course on Probability Theory - Brossura

Bhattacharya, Rabi; Waymire, Edward C.

Brossura

ISBN 10: 0387719385 ISBN 13: 9780387719382

Casa editrice: Springer Nature, 2010

Riassunto

Introductory Probability is a pleasure to read and provides a fine answer to the question: How do you construct Brownian motion from scratch, given that you are a competent analyst? There are at least two ways to develop probability theory. The more familiar path is to treat it as its own discipline, and work from intuitive examples such as coin flips and conundrums such as the Monty Hall problem. An alternative is to first develop measure theory and analysis, and then add interpretation. Bhattacharya and Waymire take the second path.

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Recensione

"The mentioned prerequisites are exposure to measure theory and analysis. Three appendices (29 pages) provide a brief but thorough introduction to the measure theory and functional analysis that is needed. ... This well-written book is full of wonderful probability theory." --Kenneth A. Ross, MathDL, February, 2008

Dalla quarta di copertina

The book develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. With this goal in mind, the pace is lively, yet thorough. Basic notions of independence and conditional expectation are introduced relatively early on in the text, while conditional expectation is illustrated in detail in the context of martingales, Markov property and strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two highlights. The historic role of size-biasing is emphasized in the contexts of large deviations and in developments of Tauberian Theory.

The authors assume a graduate level of maturity in mathematics, but otherwise the book will be suitable for students with varying levels of background in analysis and measure theory. In particular, theorems from analysis and measure theory used in the main text are provided in comprehensive appendices, along with their proofs, for ease of reference.

Rabi Bhattacharya is Professor of Mathematics at the University of Arizona. Edward Waymire is Professor of Mathematics at Oregon State University. Both authors have co-authored numerous books, including the graduate textbook, Stochastic Processes with Applications.

Dettagli dell?edizione

• Editore: Springer Nature
• Data di pubblicazione: 2010
• ISBN 10: 0387719385
• ISBN 13: 9780387719382
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 210