Electronic Journal of Probability

A Fourier analytic approach to pathwise stochastic integration

Massimiliano Gubinelli, Peter Imkeller, and Nicolas Perkowski

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Abstract

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.

Article information

Source
Electron. J. Probab., Volume 21 (2016), paper no. 2, 37 pp.

Dates
Received: 15 October 2014
Accepted: 18 December 2015
First available in Project Euclid: 3 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1454514662

Digital Object Identifier
doi:10.1214/16-EJP3868

Mathematical Reviews number (MathSciNet)
MR3485344

Zentralblatt MATH identifier
1338.60139

Subjects
Primary: 60H05: Stochastic integrals 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
paracontrolled calculus Schauder functions rough paths stochastic integration stochastic differential equations

Rights
Creative Commons Attribution 4.0 International License.

Citation

Gubinelli, Massimiliano; Imkeller, Peter; Perkowski, Nicolas. A Fourier analytic approach to pathwise stochastic integration. Electron. J. Probab. 21 (2016), paper no. 2, 37 pp. doi:10.1214/16-EJP3868. https://projecteuclid.org/euclid.ejp/1454514662


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