Brownian Motion

Sidney I. Resnick
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Sidney I. Resnick: Cornell University, School of Operations Research and Industrial Engineering

Chapter Chapter 6 in Adventures in Stochastic Processes, 2002, pp 482-557 from Springer

Abstract: Abstract THE BROWNIAN motion process, sometimes called the Wiener pro-cess, was originally posed by the English botanist Robert Brown as a model for the motion of a small particle immersed in a liquid and thus subject to molecular collisions. Brownian motion assumes a central role in the modern theory of stochastic processes and in the modern large sample theory of statistics. It is basic to descriptions of financial markets, the construction of a large class of Markov processes called diffusions, approximations to many queueing models and the calculation of asymptotic distributions in large sample statistical estimation problems.

Keywords: Brownian Motion; Invariance Principle; Iterate Logarithm; Standard Brownian Motion; Independent Increment (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-1-4612-0387-2_6

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