20.500.12556/RUL-154963 Stationary local random countable sets over the Wiener noise The times of Brownian local minima, maxima and their union are three distinct examples of local, stationary, dense, random countable sets associated with classical Wiener noise. Being local means, roughly, determined by the local behavior of the sample paths of the Brownian motion, and stationary means invariant relative to the Lévy shifts of the sample paths. We answer to the affirmative Tsirelson’s question, whether or not there are any others, and develop some general theory for such sets. An extra ingredient to their structure, that of an honest indexation, leads to a splitting result that is akin to the Wiener–Hopf factorization of the Brownian motion at the minimum (or maximum) and has the latter as a special case. Sets admitting an honest indexation are moreover shown to have the property that no stopping time belongs to them with positive probability. They are also minimal: they do not have any non-empty proper local stationary subsets. Random sets, of the kind studied in this paper, honestly indexed or otherwise, give rise to nonclassical one-dimensional noises, generalizing the noise of splitting. Some properties of these noises and the inter-relations between them are investigated. In particular, subsets are connected to subnoises. random countable sets two-sided Brownian motion locality stationarity zero-one law thick sets splitting noise spectral measure true false true Angleški jezik Ni določen Članek v reviji 2024-03-12 09:30:03 2024-03-12 09:30:06 2024-03-13 16:34:02 0000-00-00 00:00:00 2024 0 0 Str. 1063-1129 iss. 3/4 Vol. 188 Apr. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.2 0178-8051 10.1007/s00440-023-01227-3 166137603 s00440-023-01227-3-2.pdf s00440-023-01227-3-2.pdf 1 C520EC443F1D23D78C452D86CB32E9B0 d792d0a49bcd93a6d5500c62a170298c334cded297639038ea46d8774f7b4001 ea1ce3fe-e04a-11ee-a296-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=181645 https://link.springer.com/article/10.1007/s00440-023-01227-3 1 bc6a1123-e04a-11ee-a296-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=181644 Fakulteta za matematiko in fiziko 0 0 0