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.
KeywordsBrownian Motion Invariance Principle Iterate Logarithm Standard Brownian Motion Independent Increment
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