Timeline for Solve SDE $dX_t=(c+\sigma_\zeta W'_t)X_tdt + \sigma_\epsilon dW_t$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 15, 2016 at 23:34 | comment | added | Nawaf Bou-Rabee | I'm not sure what else to add to the pathwise unique solution that I wrote down. It is a fairly explicit formula for the solution to the given SDE. | |
| Dec 15, 2016 at 21:06 | comment | added | Julian Karch | Damn, I made a mistakes with the brackets. I have fixed it. It would be great if you could help me again and even better point me to the methods you have used such that i can unterstand how you obtained the solution. | |
| Sep 1, 2016 at 13:58 | comment | added | Nawaf Bou-Rabee | To be clear, this answer gives an explicit formula for the pathwise unique solution to the given SDE with random coefficients. | |
| Sep 1, 2016 at 13:16 | comment | added | Nawaf Bou-Rabee | No. Even in the special case $\sigma_{\epsilon}=0$, the solution process is not Gaussian in general. However, you can use the formula to calculate higher moments of the solution; it's a bit tedious though. | |
| Sep 1, 2016 at 13:11 | comment | added | Julian Karch | Great. You provided a formula for the first the expectation of every $X_t$. Is it also possible to state the distribution of every $X_t$? Such as $X_t$ is a Gaussian Process with this mean function and that covariance function? | |
| Aug 31, 2016 at 0:44 | history | answered | Nawaf Bou-Rabee | CC BY-SA 3.0 |