Timeline for First hitting time for non-homogeneous diffusion martingale
Current License: CC BY-SA 4.0
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| Oct 8, 2021 at 15:00 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 8, 2021 at 14:29 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 8, 2021 at 11:50 | comment | added | Iosif Pinelis | @GJC20 : I am glad this was of help. | |
| Oct 8, 2021 at 11:50 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 8, 2021 at 5:28 | vote | accept | GJC20 | ||
| Oct 8, 2021 at 5:27 | comment | added | GJC20 | Your solution is really amazing. Thanks infinitely for your help | |
| Oct 8, 2021 at 0:09 | comment | added | Iosif Pinelis | @GJC20 : I have added a piece on a uniform Hölder continuity. | |
| Oct 8, 2021 at 0:08 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 7, 2021 at 23:59 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 7, 2021 at 22:33 | comment | added | GJC20 | You have taken $\alpha=1/2$ in your reasoning, and we see $t\mapsto \mathbb P[\tau>t]$ is not uniformly $1/2-$Holder continuous (nearby zero). However, if we choose $\alpha=1/4$, then we may expect the uniform $1/4-$Holder continuity. To do so, it suffices to use an alternative estimate for the probability $\mathbb P[M\le -x|X_t=x]=\mathbb P[-M\ge x|X_t=x]=\mathbb P[(-M)^{\alpha}\ge x^{\alpha}|X_t=x]$. If you don't mind, could you please modify your arguments to obtain the uniform $\alpha-$Holder continuity? | |
| Oct 7, 2021 at 22:07 | comment | added | GJC20 | Thank you so kindly for your answer. Indeed I saw your post (mathoverflow.net/questions/405624/…) which I believe is relevant to my question. This question is related to my current project (on mean field games). I'm happy to acknowledge your help in our paper if you don't mind | |
| Oct 7, 2021 at 21:38 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |