Timeline for Does the convergence of $f_n$ imply the convergence of $\mathbb P[\inf_{0\le s\le t}(W_s-f_n(s))\le 0]$?
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| Oct 16 at 16:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 18 at 15:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
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| Jun 29, 2022 at 10:48 | answer | added | user478657 | timeline score: 0 | |
| Jun 29, 2022 at 8:34 | comment | added | user478657 | @ThomasKojar Thanks for the comment. Do you mind to specify a bit more? | |
| Jun 29, 2022 at 8:27 | history | edited | user478657 | CC BY-SA 4.0 |
added 36 characters in body
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| Jun 29, 2022 at 8:07 | history | edited | user478657 | CC BY-SA 4.0 |
added 36 characters in body
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| Jun 29, 2022 at 8:06 | comment | added | user478657 | @JamesMartin Thanks for pointing out this mistake. Yes, this is a trivial situation and I have made the modification | |
| Jun 28, 2022 at 18:25 | comment | added | Thomas Kojar | the infimum has continuity properties so you can probably just use usual measure continuity williewong.wordpress.com/2011/11/01/continuity-of-the-infimum. Otherwise, try some version of dominated/monotone convergence. | |
| Jun 28, 2022 at 18:13 | comment | added | James Martin | Something seems wrong with the set-up. Already $W_0=0$, and $f_n(0)\geq 0$, $f(0)\geq 0$, so all the probabilities are $1$. | |
| Jun 28, 2022 at 17:24 | history | asked | user478657 | CC BY-SA 4.0 |