Foundations of Modern Probability

Foundations of Modern Probability by Olav Kallenberg.

From the reviews of the first edition: "... To sum it up, one can perhaps see a distinction among advanced probability books into those which are original and path-breaking in content, such as Levy's and Doob's well-known examples, and those which aim primarily to assimilate known mat...

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Bibliographic Details
Main Author: Kallenberg, Olav (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 1997.
Edition:1st ed. 1997.
Series:Probability and Its Applications,
Springer eBook Collection.
Subjects:
Probabilities.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • Elements of Measure Theory
  • Processes, Distributions, and Independence
  • Random Sequences, Series, and Averages
  • Characteristic Functions and Classical Limit Theorems
  • Conditioning and Disintegration
  • Martingales and Optional Times
  • Markov Processes and Discrete-Time Chains
  • Random Walks and Renewal Theory
  • Stationary Processes and Ergodic Theory
  • Poisson and Pure Jump-Type Markov Processes
  • Gaussian Processes and Brownian Motion
  • Skorohod Embedding and Invariance Principles
  • Independent Increments and Infinite Divisibility
  • Convergence of Random Processes, Measures, and Sets
  • Stochastic Integrals and Quadratic Variation
  • Continuous Martingales and Brownian Motion
  • Feller Processes and Semigroups
  • Stochastic Differential Equations and Martingale Problems
  • Local Time, Excursions, and Additive Functionals
  • One-Dimensional SDEs and Diffusions
  • PDE-Connections and Potential Theory
  • Predictability, Compensation, and Excessive Functions
  • Semimartingales and General Stochastic Integration.

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