Timeline for Brownian local time density
Current License: CC BY-SA 3.0
9 events
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| Sep 9, 2015 at 23:34 | comment | added | petrelharp | This paper by Takacs gives an explicit density for $L(1,x)$ being $(2\Phi(x+u)-1)du$. | |
| May 1, 2015 at 15:58 | history | edited | Did | CC BY-SA 3.0 |
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| Jul 18, 2014 at 22:10 | comment | added | lost1 | Please have look at this link: math.stackexchange.com/questions/682825/… it is not my question but I did not find answer on Google. I thought if you integrate $L^x_1$ against the indicator function $1_{x>0}$, you get the time spent above the 0 for a Brownian motion. Can probably do something like this Brownian bridge too, but I do not think the representation is particularly useful. | |
| Jul 18, 2014 at 20:20 | comment | added | Did | @lost1 No, the local time at 0 does not say anything about the distribution of the time spent above 0. Is this your question? (And no I had not seen the MSE question, whose answer is entirely standard.) | |
| Jul 18, 2014 at 16:08 | comment | added | lost1 | have you ever seen: math.stackexchange.com/questions/682825/… I found statistics.berkeley.edu/sites/default/files/tech-reports/… which is about the local time of a Brownian Bridge but I cannot see how local time can tell us anything about about time spent above 0 except the mean. | |
| Feb 27, 2011 at 6:26 | history | edited | Did | CC BY-SA 2.5 |
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| Feb 26, 2011 at 9:47 | history | edited | Did | CC BY-SA 2.5 |
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| Feb 26, 2011 at 9:17 | history | edited | Did | CC BY-SA 2.5 |
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| Feb 26, 2011 at 8:12 | history | answered | Did | CC BY-SA 2.5 |