Gopinath Kallianpur, P. Sundar
Abstract
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.
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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.
Key concepts: Quadratic variation, Brownian excursion, Reflected Brownian motion, Reflection principle (Wiener process), Brownian motion, Martingale representation theorem, Mathematics, Fractional Brownian motion