A Basic Course in Probability Theory

Buch | Softcover
220 Seiten
2007
Springer-Verlag New York Inc.
978-0-387-71938-2 (ISBN)

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A Basic Course in Probability Theory - Rabi Bhattacharya, Edward C. Waymire
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A lively book that is a pleasure to read, this work gives analysts the tools to construct Brownian motion from scratch. It includes a complete overview of basic measure theory as well as analysis with proofs.
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.

Random Maps, Distribution, and Mathematical Expectation.- Independence, Conditional Expectation.- Martingales and Stopping Times.- Classical Zero-One Laws, Laws of Large Numbers and Deviations.- Weak Convergence of Probability Measures.- Fourier Series, Fourier Transform, and Characteristic Functions.- Classical Central Limit Theorems.- Laplace Transforms and Tauberian Theorem.- Random Series of Independent Summands.- Kolmogorov's Extension Theorem and Brownian Motion.- Brownian Motion: The LIL and Some Fine-Scale Properties.- Skorokhod Embedding and Donsker's Invariance Principle.- A Historical Note on Brownian Motion.

Reihe/Serie Universitext
Zusatzinfo biography
Verlagsort New York, NY
Sprache englisch
Maße 156 x 234 mm
Gewicht 327 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
ISBN-10 0-387-71938-5 / 0387719385
ISBN-13 978-0-387-71938-2 / 9780387719382
Zustand Neuware
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