Timeline for How to prove Feller property without using heat kernel estimates
Current License: CC BY-SA 3.0
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| Sep 5, 2017 at 10:23 | comment | added | Mateusz Kwaśnicki | Oh, now this is a completely different question! I would expect that if your domain has sufficiently narrow (infinite) "horns", you cannot hope for the Feller property. Indeed, the first coordinate of a reflecting BM in a horn $\{(x,y):x>0,|y|<H(x)\}$ behaves roughly as the one-dimensional BM with drift $H'(x)/(2 H(x))$, so choosing $H(x)=\exp(-x^4)$ should produce a counterexample. For a more detailed discussion, see p. 5 of Pinsky's article. | |
| Sep 5, 2017 at 9:57 | comment | added | sharpe | Thank you for your comment. What I particularly care about is Feller property (in my sense) of a reflecting Brownian motions on smooth domains. I edited the article to explain the details. | |
| Sep 5, 2017 at 9:38 | history | answered | Mateusz Kwaśnicki | CC BY-SA 3.0 |