Quadratic variation is the reason why you can't approximate a "jumpy" function as a 1st order taylor expansion, no matter how small you make the interval. It won't happen. Because the …

Also if you are interested in a more precise result for BM, i.e. the "largest" $\varphi$ s.t. BM has finite $\varphi$-variation a.s., you can find in the paper "Exact asymptotic estimates of …

2019年5月21日 · Let B be Brownian motion. Use Itos formula to compute the quadratic variation of $\\left[X_t^i\\right]$ for $\\left[X_t^1\\right]=e^{B_t}$, $\\left[X_t^2\\right]=\\ln ...

2019年7月25日 · Quadratic variation looks a bit like a squared norm, so why not prove the rectangle equality to prove it's given by a scalar product? $\endgroup$ – Jakobian …

2021年8月2日 · Would you mind to elaborate intuition on the following: why total variation for a continuous and differentiable function is a positive number, but quadratic variation is always 0? …

2015年8月10日 · Use $[X] = X^2 - X^2_0 - 2X \bullet X$ (a consequence of Itô's formula) in combination with the result of step 2 to get the quadratic variation $[X]_t$. Share Cite

2020年1月24日 · The third should go to zero since the quadratic variation of a function of finite variation should be zero, the second summation I guess by the continuity of the brownian …

2016年9月30日 · $\begingroup$ Hi, The problems arise when you are taking the Quadratic Variation using the sup over all partitions and not only refining (or nested) ones. Then you …

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2018年6月14日 · Also, is the quadratic variation of $\int_0^t f(W_s) ds =0$? I have been using these formulas in my work as they seem to be generally true, but I haven't been able to prove …