Probability Theory

Mircea Grigoriu
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Mircea Grigoriu: Cornell University School of Civil and Environmental Engineering

Chapter Chapter 2 in Stochastic Calculus, 2002, pp 5-101 from Springer

Abstract: 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.

Keywords: Random Walk; Characteristic Function; Probability Space; Conditional Expectation; Sample Space (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-0-8176-8228-6_2

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