Timeline for Fictitious density of paths of diffusion processes outside the Cameron--Martin space
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Apr 6, 2014 at 23:38 | history | edited | George Lowther | CC BY-SA 3.0 |
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| Apr 5, 2014 at 1:22 | history | edited | George Lowther | CC BY-SA 3.0 |
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| Apr 4, 2014 at 2:03 | comment | added | George Lowther | I also have a proof of the general case, and have started to add it. It should also extend to a more general result where $f$ is also allowed to depend non-differentiably on time. | |
| Apr 4, 2014 at 1:57 | history | edited | George Lowther | CC BY-SA 3.0 |
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| Apr 3, 2014 at 18:13 | comment | added | Dimas Abreu Dutra | I managed to prove that for bounded variation functions outside the Cameron--Martin space the fictitious density is zero. I'm writing the proof down and will reference it here whenever I'm finished. | |
| Mar 27, 2014 at 2:21 | history | edited | George Lowther | CC BY-SA 3.0 |
typos
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| Mar 27, 2014 at 1:47 | comment | added | George Lowther | Including the drift term $f(X)$ for $X$, you can use the same idea, but there are additional terms in the Girsanov transform. Although not trivial, you should be able to handle them with standard methods. | |
| Mar 27, 2014 at 1:45 | history | edited | George Lowther | CC BY-SA 3.0 |
typos
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| Mar 27, 2014 at 1:34 | comment | added | Dimas Abreu Dutra | Very clever solution, in particular that the Girsanov transformation is performed with the smooth mollification of $\phi$ and integration by parts can be used. I believe that this can be adapted to $f\in C^2_b$, as the Girsanov transformation is used in a similar way. I'll post here when I make more progress. | |
| Mar 27, 2014 at 1:30 | vote | accept | Dimas Abreu Dutra | ||
| Mar 27, 2014 at 1:30 | history | bounty ended | Dimas Abreu Dutra | ||
| Mar 26, 2014 at 23:23 | history | answered | George Lowther | CC BY-SA 3.0 |