Path Regularity of the Brownian Motion and the Brownian Sheet

Kempka H, Schneider C, Vybíral J (2023)

Publication Language: English

Publication Type: Journal article

Publication year: 2023

Journal

Constructive Approximation Springer Verlag (Germany)

Book Volume: 59

Pages Range: 485-539

DOI: 10.1007/s00365-023-09647-z

Abstract

By the work of P. Lévy, the sample paths of the Brownian motion are known to satisfy a certain Hölder 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 Lévy, 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.

Authors with CRIS profile

Cornelia Schneider Lehrstuhl für Angewandte Mathematik (Wissenschaftliches Rechnen)

Involved external institutions

Ernst-Abbe-Hochschule Jena / University of Applied Sciences DE Germany (DE) Univerzita Karlova v Praze / Charles University in Prague CZ Czech Republic (CZ)

How to cite

APA:

Kempka, H., Schneider, C., & Vybíral, J. (2023). Path Regularity of the Brownian Motion and the Brownian Sheet. Constructive Approximation, 59, 485-539. https://doi.org/10.1007/s00365-023-09647-z

MLA:

Kempka, H., Cornelia Schneider, and Jan Vybíral. "Path Regularity of the Brownian Motion and the Brownian Sheet." Constructive Approximation 59 (2023): 485-539.

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