Construction and Skorohod representation of a fractional K-rough path
Probability
2016-07-20 v1
Abstract
We go ahead with the study initiated in [3] 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.
Keywords
Cite
@article{arxiv.1607.05489,
title = {Construction and Skorohod representation of a fractional K-rough path},
author = {Aurélien Deya},
journal= {arXiv preprint arXiv:1607.05489},
year = {2016}
}