A Basic Course in Probability Theory
(Sprache: Englisch)
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.
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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.
Klappentext zu „A Basic Course in Probability Theory “
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.Inhaltsverzeichnis zu „A Basic Course in Probability Theory “
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.
Bibliographische Angaben
- Autoren: Rabi Bhattacharya , Edward C. Waymire
- 2007, 220 Seiten, Maße: 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 0387719385
- ISBN-13: 9780387719382
Sprache:
Englisch
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