Timeline for Expectation of time integral of Wiener process
Current License: CC BY-SA 2.5
16 events
| when toggle format | what | by | license | comment | |
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| Sep 8, 2017 at 1:28 | history | protected | CommunityBot | ||
| Mar 30, 2013 at 5:42 | comment | added | user32630 | I think it's related to the expectation of the time integral of wiener process. I'm curious to use the first approach to find its variance. I'm the beginner in stochastic calculus. | |
| Oct 15, 2010 at 4:16 | vote | accept | Cosmonut | ||
| Oct 14, 2010 at 17:28 | history | edited | Mark Meckes | CC BY-SA 2.5 |
Corrected spelling in title
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| Oct 14, 2010 at 14:49 | comment | added | Nate Eldredge | @Cosmonut: The distribution of the running maximum is computed in section 2.8A of Karatzas and Shreve's Brownian Motion and Stochastic Calculus. Though as my answer mentions, you don't really need it here. | |
| Oct 14, 2010 at 14:47 | history | edited | Nate Eldredge | CC BY-SA 2.5 |
TeXify
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| Oct 14, 2010 at 14:44 | answer | added | Nate Eldredge | timeline score: 6 | |
| Oct 14, 2010 at 14:16 | answer | added | MarkV | timeline score: 8 | |
| Oct 14, 2010 at 7:14 | comment | added | Cosmonut | Martingales are in L1 ------------- So Fubini Thm goes through. Ok, many thanks. | |
| Oct 14, 2010 at 6:34 | comment | added | zhoraster | More appropriate for math.stackexchange.com | |
| Oct 14, 2010 at 6:32 | comment | added | zhoraster | Does not seem to be MO level question. | |
| Oct 14, 2010 at 5:34 | comment | added | Steve Huntsman | Martingales are in $L^1$. | |
| Oct 14, 2010 at 4:04 | comment | added | Cosmonut | If I have the distribution of Max{|W_s|:0<s<T}, I could try showing that its expectation if finite. This would let me validate both the approaches. If someone has a reference where this is calculated, please let me know. | |
| Oct 14, 2010 at 3:56 | comment | added | Cosmonut | If BM is a martingale, why should its time integral have zero mean ? (Although, yes, both approaches will give me an answer of 0). Also, the problems with the approaches I mentioned are valid for questions like calculating E(\Int_0_T {W_s^2 ds}) | |
| Oct 14, 2010 at 3:28 | comment | added | Steve Huntsman | Brownian motion is a martingale (en.wikipedia.org/wiki/Martingale_%28probability_theory%29); the expectation you want is always zero. Also voting to close as this would be better suited to another site mentioned in the FAQ. | |
| Oct 14, 2010 at 3:11 | history | asked | Cosmonut | CC BY-SA 2.5 |