Electronic Journal of Probability

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

Aurélien Deya

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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

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

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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

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

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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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