Timeline for Conditional Expectation given integral of a Brownian motion
Current License: CC BY-SA 4.0
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| Feb 21, 2019 at 6:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jan 22, 2019 at 3:47 | answer | added | Michael Hardy | timeline score: 1 | |
| Jan 22, 2019 at 3:30 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Jan 21, 2019 at 23:41 | comment | added | Nate Eldredge | Hint: Since $\int_a^b B_t\,dt$ is a linear functional of Brownian motion, which is a centered Gaussian process, the random variables $X = \int_1^2 B_t\,dt$ and $Y = \int_3^4 B_t\,dt$ have a joint centered Gaussian distribution. So all you need to do is find their variances and covariance, $E[X^2]$, $E[Y^2]$, $E[XY]$, which is a nice exercise in Fubini's theorem. | |
| Jan 21, 2019 at 23:10 | history | asked | user131465 | CC BY-SA 4.0 |