A Basic Course in Probability Theory

• Κύριοι συγγραφείς: Bhattacharya, Rabi (Συγγραφέας), Waymire, Edward C. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York, 2007.
• Σειρά: Universitext
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Measure theory.; Probabilities.; Probability Theory and Stochastic Processes.; Measure and Integration.; Analysis.

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 ea...

Πίνακας περιεχομένων:

• 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.