On Besov regularity and local time of the solution to the stochastic heat equation

Besov–Orlicz spaces; Haar basis; Hausdorff dimension; Hölder continuity; local times; Schauder functions; Stochastic heat equation; white noise; Statistics and Probability; Modeling and Simulation

Abstract :

[en] Sharp Besov regularities in time and space variables are investigated for (Formula presented.), the mild solution to the stochastic heat equation driven by space–time white noise. Existence, Hölder continuity, and Besov regularity of local times are established for (Formula presented.) viewed either as a process in the space variable or time variable. Hausdorff dimensions of their corresponding level sets are also obtained.

Disciplines :

Mathematics

Author, co-author :

Boufoussi, Brahim; Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakesh, Morocco

NACHIT, Yassine ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakesh, Morocco

External co-authors :

yes

Language :

English

Title :

On Besov regularity and local time of the solution to the stochastic heat equation

Publication date :

2023

Journal title :

Stochastics: an International Journal of Probablitiy and Stochastic Processes

ISSN :

1744-2508

eISSN :

1744-2516

Publisher :

Taylor and Francis Ltd.

Volume :

Issue :

Pages :

1120 - 1145

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://www.tandfonline.com/doi/pdf/10.1080/17442508.2022.2164696

Funding text :

The authors would like to thank the associate editor and an anonymous referee for several helpful corrections and suggestions that led to many improvements in the paper. The first author would like to warmly thank Professor M. Dozzi for his fruitful discussions on an earlier version of this article.

Available on ORBilu :

since 30 November 2023

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