Timeline for Wald identity for continuous stochastic process
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 12, 2019 at 18:53 | comment | added | Mateusz Kwaśnicki | (2) For general local martingales $M_t$, $\mathbb{E} M_\tau = 0$ is a consequence of the optional stopping theorem (given appropriate integrability conditions, of course), while $\mathbb{E} M_\tau^2 = \mathbb{E} \mathbb \langle M\rangle_\tau$ is a consequence of $M_t^2 - \langle M\rangle_t$ being a martingale. | |
| Apr 12, 2019 at 18:53 | comment | added | Mateusz Kwaśnicki | Two comments: (1) For the Brownian motion, this is a very classical fact, and can be proved by standard approximation of a stopping time by 'discretized' stopping times (taking finitely many values), using the discrete Wald's identity, and passing to the limit. I am sure numerous textbooks on Brownian motion include this result. | |
| Apr 12, 2019 at 18:46 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |