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2017 Construction and Skorohod representation of a fractional $K$-rough path
Aurélien Deya
Electron. J. Probab. 22: 1-40 (2017). DOI: 10.1214/17-EJP69


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.


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Aurélien Deya. "Construction and Skorohod representation of a fractional $K$-rough path." Electron. J. Probab. 22 1 - 40, 2017.


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

zbMATH: 1368.60066
MathSciNet: MR3666015
Digital Object Identifier: 10.1214/17-EJP69

Primary: 60G22 , 60H07 , 60H15

Keywords: Fractional noise , Malliavin calculus , regularity structures theory , Rough paths theory , stochastic PDEs

Vol.22 • 2017
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