Timeline for Is a random walk sample path dense in a finite region with reflecting boundaries?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 13, 2012 at 11:33 | comment | added | Did | @covstat: You are welcome. Why did you choose this site to ask the question, rather than math.stackexchange? | |
| Feb 11, 2012 at 2:26 | comment | added | Douglas Zare | In dimension $1$, you can calculate the probability that a Brownian motion will have hit both boundaries by time $t$. | |
| Feb 10, 2012 at 19:40 | comment | added | covstat | @Didier Piau: I think you've answered it. Thank you. | |
| Feb 10, 2012 at 16:06 | comment | added | Did | The random path up to a given finite time is not dense in the cube. The full random path is (almost surely) dense in the cube, in every dimension. This is basically a consequence of Kolmogorov zero-one law: for every tiny part $S$ of the box, the path of time-length $1$ visits $S$ with probability at least $u>0$, uniformly over its starting point. Iterating this, one sees that $S$ is never visited before time $n$ with probability at most $(1-u)^n\to0$. | |
| Feb 10, 2012 at 15:53 | comment | added | covstat | I edited the question. | |
| Feb 10, 2012 at 15:51 | history | edited | covstat | CC BY-SA 3.0 |
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| Feb 10, 2012 at 2:49 | comment | added | JRN | @covstat, are you sure you want a random walk and not a billiard path? | |
| Feb 10, 2012 at 1:56 | comment | added | Yemon Choi | If the question is asked on MSE then it should give more details about the tacit assumptions, as per Nate Eldredge's comments. Without specifying the law of your stochastic process the question is ill-posed | |
| Feb 10, 2012 at 0:58 | comment | added | Nate Eldredge | This question is probably better suited for math.stackexchange.com as it is not really research level. Also, "random walk" usually refers to a process moving in discrete space; perhaps you are thinking of Brownian motion? | |
| Feb 10, 2012 at 0:17 | history | asked | covstat | CC BY-SA 3.0 |