Timeline for Characteristic exponent after Girsanov transformation
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 20, 2023 at 11:47 | comment | added | user479223 | Under $\mu$ we have that $B_t=\int_0^t f(s, \{B_s'\}_{0\leq s'\leq s}) ds+\tilde B_t$ where $\tilde B_t$ is a BM under $\mu$. I just relabel the variable $B$ as $X$. I am not sure about the characteristic function being real valued. I | |
| Jul 20, 2023 at 9:29 | comment | added | Benjamin | And one easier question: Do you have a reference for such a statement? It does not seem completely obvious to me, why I can replace $B$ by $X$ in the argument of $f$ for the SDE. | |
| Jul 20, 2023 at 5:25 | comment | added | Benjamin | Thank you for the answer, rephrasing as an SDE might help my application in the end. One small additional question: is there a way to guarantee that the characteristic function obtained this way is real-valued (if I assume $X_0=0$)? This would be most important for the application I have in mind. | |
| Jul 20, 2023 at 5:21 | vote | accept | Benjamin | ||
| Jul 19, 2023 at 11:53 | history | answered | user479223 | CC BY-SA 4.0 |