Timeline for A question about Stroock's notes on the Weyl lemma
Current License: CC BY-SA 4.0
6 events
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| Mar 2, 2020 at 22:12 | comment | added | 5th decile | I may again misunderstand his purposes (or just be mistaken). But I see no other occurrence in the subsequent discussion where facts about the dependence on $(t,x)$ seem to matter. | |
| Mar 2, 2020 at 22:10 | comment | added | 5th decile | I see, but why is the continuity of that dependence on $(t,x)$ and its uniform convergence on compact $x$-regions relevant in the immediate sequel of the discussion? I.e. he writes " Moreover, because, uniformly on compacts, $\langle L_y\phi, \Gamma(\{\tau\}_n,y) \rangle \to L\phi$". I don't see why you have to bother about the $x$-dependence to establish that fact (rather the increasing concentration of $\Gamma(\{\tau\}_n,y)$ seems what matters). | |
| Mar 2, 2020 at 21:48 | comment | added | Martin Hairer | I don't think that he ever claims that the $P(t,x)$ have a continuous density, but that the continuity he's referring to is the continuity $(t,x) \mapsto P(t,x)$ from $\mathbb{R}^{N+1}$ into the space of probability measures (with the topology of weak convergence). | |
| Mar 2, 2020 at 19:14 | history | edited | 5th decile | CC BY-SA 4.0 |
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| Mar 2, 2020 at 19:03 | history | edited | 5th decile | CC BY-SA 4.0 |
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| Mar 2, 2020 at 18:50 | history | asked | 5th decile | CC BY-SA 4.0 |