Matija Vidmar: Stationary local random countable sets over the Wiener noise
V četrtek, 1. 12. 2022 ob14:15, bo v predavalnici 2.03 na FMF, Jadranska 21, potekalo predavanje Matije Vidmarja Stationary local random countable sets over the Wiener noise.
Povzetek: The times of Brownian local minima, maxima and their union are three distinct examples of local stationary (meaning, roughly: determined by the local behavior of the sample paths, and invariant relative to the Lévy shifts of the sample paths, respectively) dense random countable sets of the classical Wiener noise. We answer to the affirmative Tsirelson's question, whether or not there are any others, and procure a kind of general theory for such sets. An extra property of honesty'' (or rather, of admitting anhonest 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 be thick: no stopping time belongs to them with positive probability; and minimal: they do not have any non-empty proper local stationary subsets. (Joint work with Jon Warren.)
Zaenkrat je predvideno, da bo predavanje potekalo v živo, bo pa organiziran tudi prenos prek videokonferenčnega sistema ZOOM. https://uni-lj-si.zoom.us/j/95492285750 ID: 954 9228 5750 Vljudno vabljeni!