Timeline for Skewness of the integral of a stochastic process
Current License: CC BY-SA 3.0
2 events
| when toggle format | what | by | license | comment | |
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| Aug 9, 2016 at 11:26 | comment | added | egg | $$E[X(t)X(u)X(v)] = M(1,1,1) = \exp\left(\mu(1+1+1) + \frac{1}{2}(1,1,1)^T\boldsymbol\Sigma(1,1,1)\right)$$ $$= \exp\left(3\mu + \frac{\sigma^2}{2}(1,1,1)^T\boldsymbol\rho(1,1,1)\right)$$ $$\boldsymbol\rho = \begin{bmatrix} 1 & \rho(t-u) & \rho(t-v)\\ \rho(t-u) & 1 & \rho(u-v) \\ \rho(t-v) & \rho(u-v) & 1 \end{bmatrix} $$ $$= \exp\left(3\mu + \frac{\sigma^2}{2}\left(3+2(\rho(t-u) + \rho(t-v)+\rho(v-u)\right)\right)$$ I think I need to triple integrate this now. | |
| Aug 9, 2016 at 9:12 | history | answered | Jarle Tufto | CC BY-SA 3.0 |