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On the Fourier analytic structure of the Brownian graph
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dc.contributor.author | Fraser, Jonathan MacDonald | |
dc.contributor.author | Sahlsten, Tuomas | |
dc.date.accessioned | 2017-10-13T13:30:07Z | |
dc.date.available | 2017-10-13T13:30:07Z | |
dc.date.issued | 2018 | |
dc.identifier | 251061378 | |
dc.identifier | f0b1237c-92f9-4d59-9612-959183b1bd4a | |
dc.identifier | 85032263781 | |
dc.identifier | 000429119200003 | |
dc.identifier.citation | Fraser , J M & Sahlsten , T 2018 , ' On the Fourier analytic structure of the Brownian graph ' , Analysis & PDE , vol. 11 , no. 1 , pp. 115-132 . https://doi.org/10.2140/apde.2018.11.115 | en |
dc.identifier.issn | 1948-206X | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/58285483 | |
dc.identifier.uri | https://hdl.handle.net/10023/11846 | |
dc.description.abstract | In a previous article (Int. Math. Res. Not. 2014:10 (2014), 2730–2745) T. Orponen and the authors proved that the Fourier dimension of the graph of any real-valued function on R is bounded above by 1. This partially answered a question of Kahane (1993) by showing that the graph of the Wiener process Wt (Brownian motion) is almost surely not a Salem set. In this article we complement this result by showing that the Fourier dimension of the graph of Wt is almost surely 1. In the proof we introduce a method based on Itô calculus to estimate Fourier transforms by reformulating the question in the language of Itô drift-diffusion processes and combine it with the classical work of Kahane on Brownian images. | |
dc.format.extent | 18 | |
dc.format.extent | 637930 | |
dc.language.iso | eng | |
dc.relation.ispartof | Analysis & PDE | en |
dc.subject | Brownian motion | en |
dc.subject | Wiener process | en |
dc.subject | Itô calculus | en |
dc.subject | Itô drift-diffusion process | en |
dc.subject | Fourier transform | en |
dc.subject | Fourier dimension | en |
dc.subject | Salem set | en |
dc.subject | Graph | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | BDC | en |
dc.subject | R2C | en |
dc.subject.lcc | QA | en |
dc.title | On the Fourier analytic structure of the Brownian graph | en |
dc.type | Journal article | en |
dc.contributor.sponsor | The Leverhulme Trust | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.2140/apde.2018.11.115 | |
dc.description.status | Peer reviewed | en |
dc.identifier.grantnumber | RF-2016-500 | en |
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