Mathematics, Stochastic Modelling, Quantitative Finance, Finance, Probability.
the interval [0,𝑇] with max⁡(𝑡(i)−𝑡(𝑖−1))→0 as 𝑛→∞ For Brownian motion, the quadratic variation over [0,𝑇] is: Derivation of (𝑑𝑊)² = dt To see why (𝑑𝑊)² = 𝑑𝑡, consider a small increment of time Δ𝑡. The increment Δ𝑊𝑡 over this interval is: When we take the limit as Δt→0, we consider dWt​ to be an