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A Fourier analytic approach to pathwise stochastic integration

Gubinelli, Massimiliano; Imkeller, Peter; Perkowski, Nicolas (2016), A Fourier analytic approach to pathwise stochastic integration, Electronic Journal of Probability, 21, p. 37 p.. 10.1214/16-EJP3868

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1410.4006v1
Date
2016
Journal name
Electronic Journal of Probability
Volume
21
Publisher
Electronic Journal of Probability and Electronic Communications in Probability
Published in
Paris
Pages
37 p.
Publication identifier
Metadata
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Author(s)
Gubinelli, Massimiliano
Imkeller, Peter
Perkowski, Nicolas
Abstract (EN)
We develop a Fourier analytic approach to rough path integration, based on the series decomposition of continuous functions in terms of Schauder functions. Our approach is rather elementary, the main ingredient being a simple commutator estimate, and it leads to recursive algorithms for the calculation of pathwise stochastic integrals, both of Itô and of Stratonovich type. We apply it to solve stochastic differential equations in a pathwise manner.
Subjects / Keywords
Fourier approach; stochastic differential equations; pathwise stochastic integration