A Basic Course in Probability Theory

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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....

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Bhattacharya, Rabi (Autor), Waymire, Edward C. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2016.
Edición:2nd ed. 2016.
Colección:Universitext,
Temas:
Probabilities.
Measure theory.
Probability Theory.
Measure and Integration.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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