Timeline for Identity involving the probability that a random walk stays below a curve
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| S Aug 2, 2020 at 8:58 | history | bounty ended | Ofir Gorodetsky | ||
| S Aug 2, 2020 at 8:58 | history | notice removed | Ofir Gorodetsky | ||
| Aug 1, 2020 at 15:03 | answer | added | Carlo Beenakker | timeline score: 5 | |
| Aug 1, 2020 at 14:49 | comment | added | Dor | Plus or minus one with probability half. It should be the same formula when we replace the discrete time random walk with a continuous time random walk, and also the same if we replace the deterministic curve with a Poisson process with rate 0.5*(N-n)^(-1/2) at time n (this might be the way to go because formulas for the exponential martingale become simpler when we make everything continuous time) | |
| Jul 31, 2020 at 20:17 | comment | added | Fedor Petrov | what is the distribution of steps? | |
| S Jul 31, 2020 at 19:44 | history | bounty started | Ofir Gorodetsky | ||
| S Jul 31, 2020 at 19:44 | history | notice added | Ofir Gorodetsky | Draw attention | |
| Jul 29, 2020 at 13:27 | history | edited | Ofir Gorodetsky | CC BY-SA 4.0 |
deleted 7 characters in body
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| Jul 27, 2020 at 9:15 | comment | added | Dor | It is not the same. The ratio between these probabilities doesn't tend to 1. However, the limit of this ratio does tend to 1 as x tends to infinity. One can compute the probability of staying below a line using the exponential martigale. I tried to do the same in here but it didn't work. | |
| Jul 27, 2020 at 7:49 | comment | added | mike | The curve is smooth at 0 (scaled to converge to Brownian motion), do you know if the probability is the same as for crossing the tangent line at 0 ? | |
| Jul 26, 2020 at 8:06 | review | First posts | |||
| Jul 26, 2020 at 9:07 | |||||
| Jul 26, 2020 at 7:55 | history | asked | Dor | CC BY-SA 4.0 |