Timeline for Constructing the 'idealized white noise' stochastic process
Current License: CC BY-SA 4.0
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| Aug 18, 2021 at 7:59 | history | edited | UserA | CC BY-SA 4.0 |
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| Aug 17, 2021 at 8:35 | history | edited | UserA | CC BY-SA 4.0 |
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| Apr 12, 2021 at 10:16 | history | edited | UserA | CC BY-SA 4.0 |
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| Apr 4, 2021 at 21:16 | history | edited | UserA | CC BY-SA 4.0 |
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| Apr 2, 2021 at 10:27 | history | edited | UserA | CC BY-SA 4.0 |
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| Apr 2, 2021 at 10:21 | history | edited | UserA | CC BY-SA 4.0 |
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| Mar 31, 2021 at 20:16 | comment | added | Abdelmalek Abdesselam | @UserA: "idealized white noise" in the book is to be understood as "heuristic/physicsy white noise". Moreover, they don't give the variance of $\dot{W}_t$ because this is a "$N(0,\infty)$" variable. The issue here is one should not take seriously the $t$-indexed process $\{\dot{W}_t\}_{t\ge 0}$. | |
| Mar 31, 2021 at 15:43 | comment | added | ofer zeitouni | I believe there is some confusion in this question: you confuse the generalized noise (which is only defined as a distribution) with its action on test functions. There is no way to define the white noise pointwise, as you wanted. | |
| Mar 31, 2021 at 15:42 | comment | added | ofer zeitouni | @Dieter Kadelka Note that the variance of $\dot{W}$ is infinite.... | |
| Mar 31, 2021 at 15:35 | answer | added | Iosif Pinelis | timeline score: 2 | |
| Mar 31, 2021 at 14:55 | history | edited | UserA | CC BY-SA 4.0 |
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| Mar 31, 2021 at 13:50 | comment | added | UserA | It is an unconventional naming I agree. I noticed it in the book Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach. I am aware that this is a generalised srochastic process. However, why is the definition of white noise if you say that the above is not white noise? | |
| Mar 31, 2021 at 13:43 | comment | added | Martin Hairer | What you call 'idealised white noise' is not white noise. It also isn't a stochastic process in the usual sense because it cannot be made measurable in $t$. | |
| Mar 31, 2021 at 12:19 | comment | added | Dieter Kadelka | Seems to be one of the most simple ways to construct white noise. | |
| Mar 31, 2021 at 11:31 | comment | added | UserA | You mean to say that we use the Kolomogorov extension theorem? | |
| Mar 31, 2021 at 11:27 | comment | added | Dieter Kadelka | What about $\otimes_{t \in \mathbb{R}_+} \mathcal{N}(0,1)$, the product of standard normal distributions? | |
| Mar 31, 2021 at 11:24 | history | edited | UserA | CC BY-SA 4.0 |
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| Mar 31, 2021 at 11:19 | history | asked | UserA | CC BY-SA 4.0 |