The quadratic variation of brownian motion and its properties
Hua Deng, Juncheng Li, Xiaolian Liao
Abstract
Hua Deng, Juncheng Li, Xiaolian Liao
Abstract
In order to research the quadratic variation better which widely used in Itô Formula and stochastic integral, the convergence of quadratic variation for classical function and Brownian motion has been proved in turn. By introducing Brownian motion and using its properties the quadratic variation of Brownian motion can be estimated. Based on the above comparisons and analyses, a dramatically different result is obtained.
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In order to research the quadratic variation better which widely used in Itô Formula and stochastic integral, the convergence of quadratic variation for classical function and Brownian motion has been proved in turn. By introducing Brownian motion and using its properties the quadratic variation of Brownian motion can be estimated. Based on the above comparisons and analyses, a dramatically different result is obtained.
Key concepts: Quadratic variation, Brownian motion, Quadratic equation, Variation (astronomy), Mathematics, Convergence (economics), Fractional Brownian motion, Brownian excursion