Brownian Motion and Gaussian Processes

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


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.


Brownian Motion Random Walk Dirichlet Problem Invariance Principle Brownian Bridge 
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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of StatisticsPurdue UniversityWest LafayetteUSA

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