Timeline for How to prove Feller property without using heat kernel estimates
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 6, 2017 at 12:40 | vote | accept | sharpe | ||
| Sep 5, 2017 at 18:51 | comment | added | Mateusz Kwaśnicki | @MartinHairer: Certainly, you are right. This is why I tried to emphasize that "now-standard" is only my impression, but apparently failed. My point was that the origin of the name is related with the $C_0$ definition. | |
| Sep 5, 2017 at 13:30 | comment | added | Martin Hairer | @Mateusz Kwaśnicki I think that what is "standard" really depends on the community you're talking to. For example, Meyn-Tweedie, Da Prato-Zabczyk and Oksendal all refer to the definition with $C_b$ when defining what a "Feller process" is and I'm sure that you have in mind just as many books going the other way around. Note though that if you take the definition with $C_0$, then "strong Feller" does not imply "Feller", which is why I personally prefer the "$C_b$" definition... | |
| Sep 5, 2017 at 9:00 | comment | added | Mateusz Kwaśnicki | Regarding the name: I believe Feller originally considered processes with compact state space; certainly Dynkin in his book on Markov processes requires a Feller process to have compact state space. Extension to locally compact spaces is then immediate via one-point compactification: this is the (now-standard, as far as I can tell) definition of the Feller property with $C_\infty$ (often denoted $C_0$). A definition that uses $C_b$ instead is sometimes referred to as the $C_b$-Feller property (for example in Niels Jacob's book). | |
| Sep 5, 2017 at 8:20 | comment | added | sharpe | Thank you for your comment. As you say this condition (1) is it too strong to prove Feller property in my strong sense. By the way, are there other good ways to prove Feller property in my strong sense? | |
| Sep 5, 2017 at 7:59 | history | answered | Martin Hairer | CC BY-SA 3.0 |