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Stochastic Analysis and Diffusion Processes$
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Gopinath Kallianpur and P Sundar

Print publication date: 2014

Print ISBN-13: 9780199657063

Published to Oxford Scholarship Online: April 2014

DOI: 10.1093/acprof:oso/9780199657063.001.0001

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Brownian Motion

Brownian Motion

(p.19) 2 Brownian Motion
Stochastic Analysis and Diffusion Processes

Gopinath Kallianpur

P. Sundar

Oxford University Press

After defining a Brownian motion (also known as a Wiener process), a standard one-dimensional Brownian motion is constructed by the use of Haar functions. Properties of a Brownian motion such as non-differentiability of almost every path, and existence of a finite quadratic variation are proved. The reflection principle and its consequences are shown.

Keywords:   Brownian motion, Brownian path, Wiener measure, reflection principle

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