Conditional Expectation and an Introduction to Martingales

J. C. Taylor
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J. C. Taylor: McGill University, Department of Mathematics and Statistics

Chapter Chapter V in An Introduction to Measure and Probability, 1997, pp 210-249 from Springer

Abstract: Abstract In this chapter, the conditional expectation operator will be defined and then used in the study of martingales. To begin, one considers the simplest cases of conditional expectation, which are closely related to conditional probability. Then, one proves the Riesz representation theorem for continuous linear functionals on Hilbert space as a tool for defining conditional expectation for square integrable random variables. Given this, it is easy to then define the conditional expectation of integrable random variables.

Keywords: Conditional Expectation; Maximal Function; Borel Function; Transition Kernel; Dyadic Interval (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1007/978-1-4612-0659-0_5

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