Brownian Motion and Gaussian Processes

Chapter
Part of the Springer Texts in Statistics book series (STS)

Abstract

We started this text with discussions of a single random variable. We then proceeded to two and more generally, a finite number of random variables. In the last chapter, we treated the random walk, which involved a countably infinite number of random variables, namely the positions of the random walk S n at times n = 0, 1, 2, 3, . The time parameter n for the random walks we discussed in the last chapter belongs to the set of nonnegative integers, which is a countable set. We now look at a special continuous time stochastic process, which corresponds to an uncountable family of random variables, indexed by a time parametert belonging to a suitable uncountable time set T. The process we mainly treat in this chapter is Brownian motion, although some other Gaussian processes are also treated briefly.

Keywords

Covariance Peris 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of StatisticsPurdue UniversityWest LafayetteUSA

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