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Stationary local random countable sets over the Wiener noise
ID
Vidmar, Matija
(
Avtor
),
ID
Warren, Jon
(
Avtor
)
PDF - Predstavitvena datoteka,
prenos
(854,89 KB)
MD5: C520EC443F1D23D78C452D86CB32E9B0
URL - Izvorni URL, za dostop obiščite
https://link.springer.com/article/10.1007/s00440-023-01227-3
Galerija slik
Izvleček
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.
Jezik:
Angleški jezik
Ključne besede:
random countable sets
,
two-sided Brownian motion
,
locality
,
stationarity
,
zero-one law
,
thick sets
,
splitting
,
noise
,
spectral measure
Vrsta gradiva:
Članek v reviji
Tipologija:
1.01 - Izvirni znanstveni članek
Organizacija:
FMF - Fakulteta za matematiko in fiziko
Status publikacije:
Objavljeno
Različica publikacije:
Objavljena publikacija
Leto izida:
2024
Št. strani:
Str. 1063-1129
Številčenje:
Vol. 188, iss. 3/4
PID:
20.500.12556/RUL-154963
UDK:
519.2
ISSN pri članku:
0178-8051
DOI:
10.1007/s00440-023-01227-3
COBISS.SI-ID:
166137603
Datum objave v RUL:
12.03.2024
Število ogledov:
314
Število prenosov:
24
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Objavi na:
Gradivo je del revije
Naslov:
Probability theory and related fields
Skrajšan naslov:
Probab. theory relat. fields
Založnik:
Springer Nature
ISSN:
0178-8051
COBISS.SI-ID:
26171392
Licence
Licenca:
CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
Povezava:
http://creativecommons.org/licenses/by/4.0/deed.sl
Opis:
To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.
Projekti
Financer:
Drugi - Drug financer ali več financerjev
Program financ.:
University of Warwick, Fernandes Fellowship
Financer:
ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
Številka projekta:
P1-0402
Naslov:
Matematična fizika
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