Electronic Journal of Probability

Construction and Skorohod representation of a fractional $K$-rough path

Aurélien Deya

Full-text: Open access

Abstract

We go ahead with the study initiated in [7] about a heat-equation model with non-linear perturbation driven by a space-time fractional noise. Using general results from Hairer’s theory of regularity structures, the analysis reduces to the construction of a so-called $K$-rough path (above the noise), a notion we introduce here as a compromise between regularity structures formalism and rough paths theory. The exhibition of such a $K$-rough path at order three allows us to cover the whole roughness domain that extends up to the standard space-time white noise situation. We also provide a representation of this abstract $K$-rough path in terms of Skorohod stochastic integrals.

Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 52, 40 pp.

Dates
Received: 21 July 2016
Accepted: 20 May 2017
First available in Project Euclid: 21 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1498010465

Digital Object Identifier
doi:10.1214/17-EJP69

Mathematical Reviews number (MathSciNet)
MR3666015

Zentralblatt MATH identifier
1368.60066

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 60G22: Fractional processes, including fractional Brownian motion 60H07: Stochastic calculus of variations and the Malliavin calculus

Keywords
stochastic PDEs fractional noise rough paths theory regularity structures theory Malliavin calculus

Rights
Creative Commons Attribution 4.0 International License.

Citation

Deya, Aurélien. Construction and Skorohod representation of a fractional $K$-rough path. Electron. J. Probab. 22 (2017), paper no. 52, 40 pp. doi:10.1214/17-EJP69. https://projecteuclid.org/euclid.ejp/1498010465


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