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....

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: Bhattacharya, Rabi (Συγγραφέας), Waymire, Edward C. (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2016.
Έκδοση:2nd ed. 2016.
Σειρά:Universitext,
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
Πίνακας περιεχομένων:
  • 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.