Abstract
This chapter illustrates the Brownian motion and stationary processes. The Brownian motion process, sometimes called the Wiener process, is one of the most useful stochastic processes in applied probability theory. This phenomenon is the motion exhibited by a small particle that is totally immersed in a liquid or gas. The process has been used beneficially in such areas as statistical testing of goodness of fit, analyzing the price levels on the stock market, and quantum mechanics. When σ = 1, the process is called standard Brownian motion. The interpretation of Brownian motion as the limit of the random walks suggests that X(t) should be a continuous function of t.
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