dc.contributor.author
Imkeller, Peter
dc.contributor.author
Perkowski, Nicolas
dc.date.accessioned
2023-10-09T08:54:48Z
dc.date.available
2023-10-09T08:54:48Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/40707
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-40428
dc.description.abstract
We approach the problem of integration for rough integrands and integrators, typically representing trajectories of stochastic processes possessing only some Hölder regularity of possibly low order, in the framework of para-control calculus. For this purpose, we first decompose integrand and integrator into Paley–Littlewood packages along the Haar–Schauder system. By careful estimation of the components of products of packages of the integrand and derivatives of the integrator we obtain a characterization of Young’s integral.
For the most interesting case of functions with Hölder regularities that sum up to an order below 1 we have to employ the concept of para-control of integrand and integrator with respect to a reference function for which a version of antisymmetric Lévy area is known to exist. This way we obtain an interpretation of the rough path integral. Lévy areas being known for most frequently used stochastic processes such as (fractional) Brownian motion, this integral serves as a basis for pathwise stochastic calculus, as the integral in classical rough path analysis.
en
dc.format.extent
20 Seiten
dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
dc.subject
Haar-Schauder series
en
dc.subject
Hölder spaces
en
dc.subject
sequence spaces
en
dc.subject
Paley-Littlewood packages
en
dc.subject
Young’s integral
en
dc.subject
rough path integral
en
dc.subject
para-control calculus
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
dc.title
A Fourier Analysis Based New Look at Integration
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation.doi
10.2478/amsil-2023-0011
dcterms.bibliographicCitation.journaltitle
Annales Mathematicae Silesianae
dcterms.bibliographicCitation.number
2
dcterms.bibliographicCitation.pagestart
149
dcterms.bibliographicCitation.pageend
168
dcterms.bibliographicCitation.volume
37
dcterms.bibliographicCitation.url
https://doi.org/10.2478/amsil-2023-0011
refubium.affiliation
Mathematik und Informatik
refubium.affiliation.other
Institut für Mathematik

refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.eissn
2391-4238
refubium.resourceType.provider
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