A Basic Course in Probability Theory

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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...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Bhattacharya, Rabi (Author), Waymire, Edward C. (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: New York, NY : Springer New York : Imprint: Springer, 2007.
Edition:1st ed. 2007.
Series:Universitext,
Subjects:
Probabilities.
Measure theory.
Mathematical analysis.
Probability Theory.
Measure and Integration.
Analysis.
Online Access:Texto Completo
Table of Contents:
  • 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.

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