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Probability Theory

In: Stochastic Calculus

Author

Listed:
  • Mircea Grigoriu

    (Cornell University School of Civil and Environmental Engineering)

Abstract

Essential concepts of probability theory needed in this text are reviewed and are illustrated by examples. The review includes the concepts of events, sample space, σ-field, measure, probability measure, probability space, conditional probability, independence, random variable and vector, integral of random variables, expectation, distribution, density, and characteristic functions, second moment properties, convergence of sequences of random variables, conditional expectation, and martingales. The readers familiar with these concepts can skip this chapter entirely. However, some of those readers may benefit from using this chapter as a summary of facts and examples needed in the rest of the book.

Suggested Citation

  • Mircea Grigoriu, 2002. "Probability Theory," Springer Books, in: Stochastic Calculus, chapter 0, pages 5-101, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-8228-6_2
    DOI: 10.1007/978-0-8176-8228-6_2
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