Timeline for Examples of a continuous martingale with $E[\sup\limits_{0\leq s\leq t} |M_s|]=\infty$?
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4 events
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| Feb 20, 2015 at 15:50 | comment | added | lost1 | No, I was looking for a martingale, not a local martingale.I am saying the conditions given are sufficient conditions for martingales. I want to see why they are not necessary conditions. | |
| Jul 22, 2014 at 7:28 | comment | added | Olivier Leveque | You could let $B$ start somewhere else than $0$, but then I agree there is always a possibility that $B$ comes back at $0$ at some point. There are similar examples in higher dimensions, where $B$ is transient, but OK, this does not guarantee that $M$ is strictly speaking continuous. Regarding your second comment, we are looking for a local martingale, not a martingale. | |
| Jul 22, 2014 at 2:35 | comment | added | Nate Eldredge | I'm confused: does $B_t$ start at 0? Then surely $M_t$ is not continuous? And aren't we looking for a martingale, not a local martingale? | |
| Jul 21, 2014 at 16:14 | history | answered | Olivier Leveque | CC BY-SA 3.0 |