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Jan 15, 2023 at 22:44 vote accept MightyPower
Jan 4, 2023 at 17:18 answer added Thomas Kojar timeline score: 1
Dec 28, 2022 at 17:13 comment added MightyPower @ThomasKojar Thank you for the comment!
Dec 27, 2022 at 22:49 comment added Thomas Kojar But if you still want low regularity for the continuous noise, then I would suggest using Local time and average density techniques eg. "Holder conditions for the local times and the Hausdorff-measure of the level sets of Gaussian random fields".
Dec 27, 2022 at 22:46 comment added Thomas Kojar if you add further regularity assumptions such C1 smoothness of the noise, then the zero set is discrete eg. "Zeros of smooth stationary Gaussian processes".
Dec 27, 2022 at 22:45 comment added Thomas Kojar for just general continuous stationary Gaussian process, there might not be any density because the zero sets can be fractal eg. see "The Exact Hausdorff Measure of the Zero Set of Certain Stationary Gaussian Processes"
Dec 27, 2022 at 19:05 history edited Daniele Tampieri CC BY-SA 4.0
Fixed a typo
Dec 27, 2022 at 19:00 history edited MightyPower CC BY-SA 4.0
added 10 characters in body
Dec 27, 2022 at 18:48 history asked MightyPower CC BY-SA 4.0