Document Type

Article

Publication Date

2011

Abstract

We study the local-in-time regularity of the Brownian motion with respect to localized variants of modulation spaces Msp,q and Wiener amalgam spaces Wsp,q. We show that the periodic Brownian motion belongs locally in time to Msp,q(T) and Wsp,q(T) for (s−1)q<−1(s−1)q<−1, and the condition on the indices is optimal. Moreover, with the Wiener measure μ on TT, we show that (Msp,q(T),μ) and (Wsp,q(T),μ) form abstract Wiener spaces for the same range of indices, yielding large deviation estimates. We also establish the endpoint regularity of the periodic Brownian motion with respect to a Besov-type space bˆp,∞s(T). Specifically, we prove that the Brownian motion belongs to bˆp,∞s(T) for (s−1)p=−1(s−1)p=−1, and it obeys a large deviation estimate. Finally, we revisit the regularity of Brownian motion on usual local Besov spaces Bp,qs, and indicate the endpoint large deviation estimates.

Publication Title

Advances in Mathematics

Volume

228

Issue

5

First Page

2943

Last Page

2981

Required Publisher's Statement

Copyright © 2015 Elsevier B.V.

doi:10.1016/j.aim.2011.07.023

Creative Commons License


This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Included in

Mathematics Commons

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