2016/07/19 by Aurélien Deya, Deya, Aurélien
Economics, Econometrics and Finance · Computer Science · Mathematics · #Stochastic processes and financial applications #Advanced Mathematical Modeling in Engineering #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1607.05489
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.