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world:exobrownian
2023/11/14 18:37

The reflection principle

Exercise Let be a standard Brownian motion and denote . Then

Let be the first time that the Brownian motion crosses the threshold . Note that since is a standard brownian motion and from this, we can show that for the almost surely finite stopping time , then is a standard brownian motion. Finally, which concludes the proof.

world/exobrownian.txt · Last modified: 2022/03/16 07:40 (external edit)