Abstract
This chapter discusses the Brownian motion. A Brownian motion or a Wiener process is a stochastic process. A Brownian motion is a martingale. Therefore, the martingale inequality can be applied to Brownian motion. There is a continuous version of a Brownian motion. Every separable Brownian motion is continuous. Almost all sample paths of a Brownian motion are nowhere differentiable. Almost all sample paths of a Brownian motion have infinite variation on any finite interval. The chapter provides an account of Brownian motion in n dimensions.
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