Timeline for What happens to an SDE conditional on the underlying Brownian motion being close to $f \in C[0, T]$?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 15 at 12:26 | comment | added | Pierre PC | @MartinHairer Of course it is... I was doing things in the wrong order, and trying to apply the theorem to the higher-order control problems... Thank you! | |
| Nov 15 at 12:13 | comment | added | Martin Hairer | @PierrePC Isn't that step just the Stroock-Varadhan support theorem? | |
| Nov 15 at 11:06 | vote | accept | Nate River | ||
| Nov 15 at 10:23 | comment | added | Martin Hairer | @PierrePC Of course you can also generate Lie brackets of higher order. Also, while rough path theory gives "simple" proofs (basically because they are already encoded in the theory), the classical area studying these kind of statements is geometric control theory. | |
| Nov 15 at 9:43 | history | edited | Pierre PC | CC BY-SA 4.0 |
Improved exposition (hopefully).
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| Nov 15 at 9:21 | comment | added | Pierre PC | I'm sure there are other proofs of the results I give that make no use of rough path theory, this is just my personal bias. I think the main takeaway is that the support contains all the solutions of the solution to the second control problem (the one involving $\beta$ and the Lie bracket) for all $w$ sufficiently close to $f$ but $\beta$ basically arbitrary. | |
| Nov 15 at 6:04 | comment | added | Nate River | I did not expect rough paths to be relevant to this problem, interesting! I will need some time to properly digest this answer, but it should give a good starting point… | |
| Nov 14 at 15:10 | history | answered | Pierre PC | CC BY-SA 4.0 |