Timeline for Local martingale but not martingale
Current License: CC BY-SA 4.0
4 events
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| Jan 6, 2021 at 22:53 | comment | added | Martin Weizenguss | I saw it as an example of a local martingale but no martingale but there was no proof attached to it and i couldn't make my mind up as to why this is. Probably the proof wasn't given in the script because it is very suitable as an exercise. Still your answer has helped me understand. Thank you very much! | |
| Jan 6, 2021 at 21:02 | comment | added | Mateusz Kwaśnicki | The event $\{B_t = -x \text{ for some } t \geqslant 0\}$ has probability zero, so $Y_t$ is indeed well-defined (with probability one). By the Itô formula one easily finds that $Y_t$ is a local martingale. Finally, $\mathbb E Y_t$ converges to zero by the dominated convergence theorem, so $Y_t$ cannot be a true martingale. (This is a standard exercise, I think, so I am not sure this question fits the guidelines of this site. Thus I leave this as a comment so that others can decide.) | |
| Jan 6, 2021 at 19:22 | history | edited | YCor | CC BY-SA 4.0 |
fixed formatting/tags
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| Jan 6, 2021 at 18:45 | history | asked | Martin Weizenguss | CC BY-SA 4.0 |