Timeline for Limit of first passage time
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 21, 2017 at 11:43 | vote | accept | avk255 | ||
| Oct 21, 2017 at 11:44 | |||||
| Jun 3, 2016 at 17:51 | comment | added | avk255 | $f$ is not continuous either. It is piecewise continuous, bounded, finite points of discontinuity. | |
| Jun 3, 2016 at 14:16 | comment | added | Joris Bierkens | How about $f$, is it not continuous either? | |
| Jun 3, 2016 at 13:55 | comment | added | avk255 | No, $\mu$ and $\sigma$ are piecewise continuous. We can assume that the number of discontinuities is finite. They are bounded, $\sigma$ is bounded from below by a strictly positive number. Hence, by Nakao, I will have a strong solution. But, I must work with piecewise continuous $\mu$ and $\sigma$. | |
| Jun 3, 2016 at 13:46 | comment | added | Joris Bierkens | Are $\mu$ and $\sigma$ locally Lipschitz and in particular continuous? In this case, further assuming you have uniqueness of the martingale solution, Kallenberg Thm 21.11 gives the Feller property. | |
| Jun 3, 2016 at 13:44 | comment | added | avk255 | Thanks for the answer. From what I know, the diffusion is not Feller continuous because the drift and volatility are piecewise Lipschitz and not Lipschitz everywhere. Also, $f$ is piecewise Lipschitz. Do you think there are some standard results like the one you are referring to that can do our job? | |
| Jun 3, 2016 at 13:25 | history | answered | Joris Bierkens | CC BY-SA 3.0 |