A Basic Course in Probability Theory
This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. In this second edition, the text has been reorganized for didactic purposes, new exercises have been added and basic theory has been expanded....
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2016, 2016
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| Edition: | 2nd ed. 2016 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Preface to Second Edition
- Preface to First Edition
- I. Random Maps, Distribution, and Mathematical Expectation
- II. Independence, Conditional Expectation
- III. Martingales and Stopping Times
- IV. Classical Central Limit Theorems
- V. Classical Zero-One Laws, Laws of Large Numbers and Large Deviations
- VI. Fourier Series, Fourier Transform, and Characteristic Functions
- VII. Weak Convergence of Probability Measures on Metric Spaces
- VIII. Random Series of Independent Summands
- IX. Kolmogorov's Extension Theorem and Brownian Motion
- X. Brownian Motion: The LIL and Some Fine-Scale Properties
- XI. Strong Markov Property, Skorokhod Embedding and Donsker's Invariance Principle
- XII. A Historical Note on Brownian Motion
- XIII. Some Elements of the Theory of Markov Processes and their Convergence to Equilibrium
- A. Measure and Integration
- B. Topology and Function Spaces
- C. Hilbert Spaces and Applications in Measure Theory
- References
- Symbol Index
- Subject Index