Timeline for How to estimate the difference between two Ito diffusions?
Current License: CC BY-SA 4.0
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| Jan 16 at 5:20 | comment | added | epsilon | Thanks a lot. I think I can use the classical Yamada & Watanabe technique (e.g., section 5.2 of Karatzas and Shreve) to derive (2). But is it possible to prove it using Ito-Tanaka formula? | |
| Jan 16 at 1:43 | comment | added | Nate Eldredge | Does it help to mollify, with a sequence of smooth functions $F_n(x,y) \to |x-y|$ in some appropriate fashion? Apply Ito's formula for each $F_n$ and try to pass to the limit. You'll probably have to bound the quadratic variation of $\left|\nabla F_n(X_t,Y_t) - \frac{X_t - Y_t}{|X_t - Y_t|} \right|$ which seems like it should be possible if $F_n$ is chosen well. | |
| Jan 15 at 20:39 | history | edited | Piotr Hajlasz | CC BY-SA 4.0 |
added 68 characters in body
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| Jan 15 at 16:33 | history | asked | epsilon | CC BY-SA 4.0 |