Timeline for Random walk with decreasing steps
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
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| Jan 4, 2022 at 20:13 | history | became hot network question | |||
| Jan 4, 2022 at 16:46 | history | edited | Sia-TeX | CC BY-SA 4.0 |
deleted 103 characters in body
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| Jan 4, 2022 at 16:37 | vote | accept | Sia-TeX | ||
| Jan 4, 2022 at 15:42 | answer | added | Iosif Pinelis | timeline score: 5 | |
| Jan 4, 2022 at 15:24 | comment | added | Sia-TeX | But here you assume that $\sum_{n \geq 1} 1/n^{2\alpha}$ converges. Which is the case when $\alpha>1/2$. I am more interested in $\alpha< 1/2,$ that we have a large variance but bounded higher moments. | |
| Jan 4, 2022 at 14:28 | comment | added | Sia-TeX | Thank you. I have $1/2>\alpha>0$ and $t$ to approach infinity. I want to to know $P( R(t) > x )$ as a function of $x, t, \alpha,$ denote by $F(x, t, \alpha).$ I hope this clarifies my question. From the information we have we can estimate all the moments, shouldn't this give us the probablity distributin? | |
| Jan 4, 2022 at 13:42 | comment | added | Iosif Pinelis | OK, I will try to help you just once more. It is not enough to say "I would like to estime this". You should specify properties of the estimate you want and terms in which you want the estimate to be expressed. Otherwise, I can just say that the best estimate of that probability is that probability itself. Generally, be quite specific. | |
| Jan 4, 2022 at 13:33 | comment | added | Sia-TeX | More percisely: I would like to estime $P( R(t)>1)$. Obviously this depends on $\alpha, t.$ | |
| Jan 4, 2022 at 13:31 | history | edited | Sia-TeX | CC BY-SA 4.0 |
added 10 characters in body
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| Jan 4, 2022 at 13:27 | comment | added | Iosif Pinelis | "understand the behaviour of" is just about as unclear as "what is". Moreover, you have another two instances of "what is" in your comment. So, it is still unclear what you want. | |
| Jan 4, 2022 at 13:27 | history | edited | Sia-TeX | CC BY-SA 4.0 |
added 18 characters in body; edited title
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| Jan 4, 2022 at 13:26 | history | edited | LSpice | CC BY-SA 4.0 |
Typos
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| Jan 4, 2022 at 13:21 | comment | added | Sia-TeX | Ok, fair enough. Let me explian more: If $\alpha=0,$ then we have a classical case, and by CLT we approach a normal distribution, meaning that about 70% of the time I expect to end up in $(-\sqrt{t}, \sqrt{t})$. But when $\alpha >0$ this changes. In general I would like to understand the behaviour of $R(t),$ for large $t.$ For example what is the probability of ending up somewhere greater than 1, $P(R(t)>1)?$ Or what is the probablity that $-1/M<R(t)<1/M$ for some $M >1$. | |
| Jan 4, 2022 at 13:10 | review | Close votes | |||
| Jan 10, 2022 at 3:09 | |||||
| Jan 4, 2022 at 13:06 | comment | added | Iosif Pinelis | Questions of the form "What is" are almost always unclear, unless the terms in which the target object is to be expressed are specified. Without such specification, the tautological answer is always possible: "It is what it is", which is probably not an answer you want. So, you should state what specifically you want to know about $R(t)$. Note also that even the expression for the pdf of the sum of iid uniformly distributed random variables is rather complicated (en.wikipedia.org/wiki/Irwin%E2%80%93Hall_distribution). | |
| Jan 4, 2022 at 12:56 | comment | added | Sia-TeX | corrected, thanks. | |
| Jan 4, 2022 at 12:55 | history | edited | Sia-TeX | CC BY-SA 4.0 |
edited body
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| Jan 4, 2022 at 12:52 | comment | added | Dieter Kadelka | I think a typo. $T = t$? | |
| S Jan 4, 2022 at 12:11 | review | First questions | |||
| Jan 4, 2022 at 12:52 | |||||
| S Jan 4, 2022 at 12:11 | history | asked | Sia-TeX | CC BY-SA 4.0 |