On a modelled rough heat equation

2014/04/22 by Deya, Aurélien
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1404.5438

Abstract

We use the formalism of Hairer's regularity structures theory \citehai-14 to study a heat equation with non-linear perturbation driven by a space-time fractional noise. Different regimes are observed, depending on the global pathwise roughness of the noise. To this end, and following the procedure exhibited in \citehai-14, the equation is first "lifted" into some abstract "regularity structure" and therein solved through a fixed-point argument. Then we construct a consistent "model" above the fractional noise, by relying on a smooth Fourier-type approximation of the process.

Related

• Construction and Skorohod representation of a fractional K-rough path
• Pathwise regularization of the stochastic heat equation with multiplicative noise through irregular perturbation
• A full discretization of the rough fractional linear heat equation
• Study of a fractional stochastic heat equation
• Regularity properties of the solution to a stochastic heat equation driven by a fractional Gaussian noise on \mathbbS²