Functions and Analysis

    

An Untold Story of Brownian Motion

Authors: Yu-Lin Chou

Although the concept of Brownian motion or Wiener process is quite popular, proving its existence via construction is a relatively deep work and would not be stressed outside mathematics. Taking the existence of Brownian motion in $C([0,1], \R)$ ``for granted'' and following an existing implicit thread, we intend to present an explicit, simple treatment of the existence of Brownian motion in the space $C([0, +\infty[, \R)$ of all continuous real-valued functions on the ray $[0, +\infty[$ with moderate technical intensity. In between the developments, some informative little results are proved.

Comments: 6 Pages. expository article

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Submission history

[v1] 2020-11-12 10:26:50

Unique-IP document downloads: 314 times

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