Quadratic Variation of Brownian Motion

stochastic-processes brownian-motion quadratic-variation

You can find a short proof of this fact (actually in the more general case of Fractional Brownian Motion) in the paper :

M. Prattelli : A remark on the 1/H-variation of the Fractional Brownian Motion. Probability Seminar Vol. XLIII (pdf)


The book Brownian Motion - An Introduction to Stochastic Processes by René Schilling & Lothar Partzsch contains a (detailed) proof of this fact.

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