Sample paths of white noise in spaces with dominating mixed smoothness

Hummel, Felix

doi:10.1007/s43037-021-00136-8

Cited by 4 publications

(2 citation statements)

References 30 publications

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“…We now recover the results of Kamont [28] (cf. also [22]) on the regularity of the sample paths of Brownian sheets. We combine the representation in (47) (or (46)) with Theorem 21 and Definition 22 in order to show that the sample paths almost surely lie in S…”

Section: Results Of Kamontmentioning

confidence: 99%

Path Regularity of the Brownian Motion and the Brownian Sheet

2023

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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.

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Section: Results Of Kamontmentioning

confidence: 99%

Path Regularity of the Brownian Motion and the Brownian Sheet

2023

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“…We now recover the results of Kamont [27] (cf. also [21]) on the regularity of the sample paths of Brownian sheets. We combine the representation in (46) (or (45)) with Theorem 21 and Definition 22 in order to show that the sample paths lie in S…”

Section: Results Of Kamontmentioning

confidence: 99%

Path regularity of Brownian motion and Brownian sheet

Kempka¹,

Schneider²,

Vybíral³

2022

Preprint

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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, where the sample paths of the Brownian motion lie in almost surely. 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.

show abstract