Path Regularity of the Brownian Motion and the Brownian Sheet

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F24%3A00374086" target="_blank" >RIV/68407700:21340/24:00374086 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00365-023-09647-z" target="_blank" >https://doi.org/10.1007/s00365-023-09647-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00365-023-09647-z" target="_blank" >10.1007/s00365-023-09647-z</a>

Result language
angličtina
Original language name
Path Regularity of the Brownian Motion and the Brownian Sheet
Original language description
By the work of P. Levy, the sample paths of the Brownian motion are known to satisfy a certain Holder regularity condition almost surely. This was later improved by Ciesielski, who studied the regularity of these paths in Besov and Besov-Orlicz spaces. We review these results and propose new function spaces of Besov type, strictly smaller than those of Ciesielski and Levy, in which the sample paths of the Brownian motion almost surely lie. In the same spirit, we review and extend the work of Kamont, who investigated the same question for the multivariate Brownian sheet and function spaces of dominating mixed smoothness.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA23-04720S" target="_blank" >GA23-04720S: Fine properties of functions, operators and function spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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