Timeline for How to find the "natural scale function" for more general stochastic processes?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 1, 2021 at 16:02 | vote | accept | MikeG | ||
| Apr 25, 2021 at 14:11 | answer | added | MikeG | timeline score: 3 | |
| Apr 25, 2021 at 13:53 | comment | added | MikeG | @NawafBou-Rabee: Oh that makes a lot of sense! Then the problem of finding the function f is reduced to solving the differential equation Lf=0, right?(So, the first step is to calculate the corresponding generator of the markov process... very reasonable!) | |
| Apr 25, 2021 at 12:02 | comment | added | Nawaf Bou-Rabee | Let $L$ be the generator of the Itô diffusion, and note that $LS = 0$. This means that $S$ is a harmonic function associated with the process. In general, for a Markov process $X_t$ with generator $L$, a non-negative function is a harmonic function if and only if $f(X_t)$ is a martingale. See, e.g., Section 1.4 of wt.iam.uni-bonn.de/fileadmin/WT/Inhalt/people/Anton_Bovier/… | |
| Apr 25, 2021 at 12:01 | comment | added | MikeG | If you need additional conditions on "Markov processes", just add them--if they don't rule out the asymmetric SRW case above. | |
| Apr 25, 2021 at 5:54 | history | asked | MikeG | CC BY-SA 4.0 |