Partial sum process of orthogonal series as rough process

Thesis

In this thesis, we investigate the pathwise regularity of partial sum process of general orthogonal series, and prove that the partial sum process is a geometric 2-rough process under the same condition as in Menshov-Rademacher Theorem. For Fourier series, the condition can be improved, and an equivalent condition on the limit function is identified.

Authors: Yang, D

• Publication date: 2012
• DOI: 10.5287/ora-7ed5qgqo1
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: Oxford University, UK
• Language: English
• Keywords: partial sum process; orthogonal series; harmonic analysis; rough path theory
• Subjects: Functional analysis (mathematics)