Timeline for Probability of general Brownian (or non) bridge to be higher than given parameter?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 5, 2017 at 17:37 | vote | accept | Alexander Chervov | ||
| May 18, 2017 at 23:30 | comment | added | ofer zeitouni | Of course it does. The probability in question is to start at $-b$ and end at $c$ w/out touching 0. The reflection principle (and a union-exclusion) tells you that this is the same as hitting $c$ w/out the constraint, minus the probability of hitting $-c$. This is what I wrote. If you prefer and are more analytcally inclined, solve the heat equation with Dirichlet boundary conditions at $0$. | |
| May 18, 2017 at 20:54 | comment | added | Alexander Chervov | Wiki does not seem to give similar reflection principle that you use | |
| May 18, 2017 at 19:59 | comment | added | ofer zeitouni | $P^b$ is the law of the process starting at $b$. The equality is just shift-invariance of increments of Brownian motion. As for reflection principle, just google it... en.wikipedia.org/wiki/Reflection_principle_(Wiener_process) | |
| May 14, 2017 at 9:39 | comment | added | Alexander Chervov | A reffrence to Reflection principle which close to your discussion and written for simplyminded persons would be also very helpful . Thanks in advance! | |
| May 14, 2017 at 9:06 | comment | added | Alexander Chervov | Thank you very much ! The answer seems to be correct - it is correct in limiting cases and also seems same (up to notations) as the paper quoted. But I am not expert in stoch.proc. so I cannot fully understand your argument with reflection principle, if you can give more details it would be very helpful. What is $P^b$ and why it equals to what you write ? | |
| May 10, 2017 at 15:33 | history | answered | ofer zeitouni | CC BY-SA 3.0 |