Timeline for Question about a Limit of Gaussian Integrals and how it relates to Path Integration (if at all)?
Current License: CC BY-SA 2.5
14 events
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| Apr 13, 2017 at 12:40 | history | edited | CommunityBot |
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| Apr 5, 2011 at 23:29 | vote | accept | jzadeh | ||
| Apr 5, 2011 at 23:16 | vote | accept | jzadeh | ||
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| Apr 4, 2011 at 23:11 | vote | accept | jzadeh | ||
| Apr 5, 2011 at 0:50 | |||||
| Apr 4, 2011 at 19:48 | answer | added | Jeff Schenker | timeline score: 3 | |
| Mar 25, 2011 at 22:53 | history | edited | jzadeh | CC BY-SA 2.5 |
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| Mar 25, 2011 at 21:09 | comment | added | jzadeh | Concerning 2) and and the comment following 3) I have been moving back and forth between analyzing the iterated density of $X_n$ and analyzing the behavior of its moment generating function and these comments really apply to the mgf. | |
| Mar 25, 2011 at 8:46 | history | edited | Did | CC BY-SA 2.5 |
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| Mar 25, 2011 at 8:42 | history | edited | jzadeh | CC BY-SA 2.5 |
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| Mar 25, 2011 at 6:56 | comment | added | jzadeh | The density of $X_n(t)$ is given by the iterated integral in ** | |
| Mar 25, 2011 at 6:56 | comment | added | jzadeh | Yes this is true if you look at this from a probabilistic perspective you can argue by self similarity. So set $X_n(t)=B_n(B_{n-1}(...(B1(t))...))$ where $B_i$ is two-sided Brownian motion. Then the following equalities hold in distribution: $X_n(t)=t^{\frac{1}{2^n}} X_n(1)$ taking limits on both sides we see that the random variable $\lim_{n\rightarrow \infty} X_n(t)$ depends only on $X_n(1)$ (i.e. is time invariant). Other authors have made this more rigorous (there is a proof that the asymptotic density is time invariant based on method of moments) | |
| Mar 25, 2011 at 5:37 | comment | added | Bjørn Kjos-Hanssen | Looks like the left hand side of (**) depends on $t$, but the right hand side does not? | |
| Mar 25, 2011 at 4:14 | history | edited | jzadeh | CC BY-SA 2.5 |
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| Mar 25, 2011 at 3:20 | history | asked | jzadeh | CC BY-SA 2.5 |