Timeline for Wiener measure of hitting sets A,B but not C (or easier hitting A but not C)
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 22, 2014 at 20:02 | vote | accept | Thomas Kojar | ||
| Sep 8, 2014 at 21:06 | answer | added | Carlo Beenakker | timeline score: 1 | |
| Jul 22, 2014 at 0:20 | history | edited | Thomas Kojar | CC BY-SA 3.0 |
added 132 characters in body; edited title
|
| Jul 22, 2014 at 0:09 | history | edited | Thomas Kojar | CC BY-SA 3.0 |
added 4 characters in body
|
| Jul 19, 2014 at 15:14 | history | edited | Thomas Kojar | CC BY-SA 3.0 |
added 79 characters in body
|
| Jul 19, 2014 at 15:14 | comment | added | Thomas Kojar | thanks Ilya. Still I would appreciate if someone can give a precise answer. | |
| Jul 17, 2014 at 20:25 | comment | added | SBF | My point was: if you take a look at the latter integral, you can't say it's less than $1$, so it's not a probability of anything - in particular not of hitting $C$. On a separate note, if you know what's the probability of hitting $B$ without touching $C$, compute this probability for initial conditions on the boundary of $A$. | |
| Jul 17, 2014 at 20:01 | history | edited | Thomas Kojar | CC BY-SA 3.0 |
added 22 characters in body
|
| Jul 17, 2014 at 19:55 | comment | added | Thomas Kojar | i want x and t to vary. I am not just looking at paths starting from fixed point x and hitting C at a fixed time t, which is what you wrote. But I will review it anyhow. | |
| Jul 17, 2014 at 19:50 | comment | added | SBF | I'm pretty sure there is a couple of neat PDEs that the solution satisfies, though likely there is also a direct approach - not that I know of unfortunately. Let's take a look at the integrals. If $p(x,y,t)$ is a density of lending at $y$ from $x$ in time $t$, then the last integral is not even a probability. $$ \int_C p(x,y,t)\mathrm dy = P(x,C,t) $$ that is a probability of landing in a set $C$ from $x$ in time $t$. Your latter integral is integrating this probability over $x\in \Bbb R$ and $t\in \Bbb R_+$ - that's not a probability of hitting $C$. | |
| Jul 17, 2014 at 19:43 | history | edited | Thomas Kojar | CC BY-SA 3.0 |
added 254 characters in body
|
| Jul 17, 2014 at 19:37 | comment | added | Thomas Kojar | that's what I was doing. I updated it. | |
| Jul 17, 2014 at 19:36 | history | edited | Thomas Kojar | CC BY-SA 3.0 |
added 254 characters in body
|
| Jul 17, 2014 at 19:30 | comment | added | SBF | I think if you express each of the integrals as a probability of a certain event, it would be easier for you to realize whether they correspond to what you want or not. | |
| Jul 17, 2014 at 19:29 | history | edited | Thomas Kojar | CC BY-SA 3.0 |
added 254 characters in body
|
| Jul 17, 2014 at 19:21 | history | asked | Thomas Kojar | CC BY-SA 3.0 |