Electronic Journal of Probability
- Electron. J. Probab.
- Volume 22 (2017), paper no. 52, 40 pp.
Construction and Skorohod representation of a fractional $K$-rough path
We go ahead with the study initiated in  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.
Electron. J. Probab., Volume 22 (2017), paper no. 52, 40 pp.
Received: 21 July 2016
Accepted: 20 May 2017
First available in Project Euclid: 21 June 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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