Timeline for When are the transition densities of an SDE symmetric?
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5 events
| when toggle format | what | by | license | comment | |
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| Oct 1, 2023 at 21:11 | comment | added | Nawaf Bou-Rabee | Yes, since the generator of the process $L_t f(x) = \nabla \cdot ( M(t,x) \nabla f(x))$ is symmetric in the $L^2$-inner product. | |
| Oct 1, 2023 at 19:57 | vote | accept | Akira | ||
| Oct 1, 2023 at 19:57 | comment | added | Akira | I have read the paper ''Time-reversible diffusions'' by Kent, but I could not see how to get your statement from Theorems 4.1 and 4.2. May I ask if $d X_t = \operatorname{div}M(t, X_t) dt + \sqrt{2} B(t, X_t) dW_t$ is symmetric if (as you defined) $M(t, x) = B(t, x) B^\intercal(t, x)$ and $(\operatorname{div} M)_i = \sum_{j=1}^n \partial M_{ij}/ \partial x_j$? | |
| Oct 1, 2023 at 16:33 | history | edited | Nawaf Bou-Rabee | CC BY-SA 4.0 |
added 401 characters in body
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| Oct 1, 2023 at 15:22 | history | answered | Nawaf Bou-Rabee | CC BY-SA 4.0 |