Timeline for Occupation time of non-stationary random walk
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 17, 2023 at 2:50 | comment | added | Andreas Haupt | One more request for a pointer: I am seeking to generalize the above argument to general random walks (i.e. non-Rademacher increments). What is a good text on reflection principle and probability of staying positive for a general random walk? | |
| Aug 24, 2021 at 16:20 | vote | accept | Andreas Haupt | ||
| Aug 24, 2021 at 15:44 | comment | added | fedja | @AndreasHaupt Sure: $P(S<B)\le\sum_{s=0^B}P(X_{T-s}=0)$, for example. As to the square root, the standard application of the reflection principle for the simple random walk yields that $P(S_1,S_2,\dots,S_{2n}>0)=2^{-2n}{2n-1\choose n-1}$ and Stirling finishes the story. | |
| Aug 24, 2021 at 14:28 | comment | added | Andreas Haupt | Thank you @fedja, this has been very helpful! Could you expand a bit why the probability of being in a particular position tending to zero implies that $S$ is large? Also, do you have a reference on the square-root statement? | |
| Aug 24, 2021 at 1:29 | history | answered | fedja | CC BY-SA 4.0 |