On a modelled rough heat equation

• 成果类型: Article
• 署名作者: Deya, Aurelien
• 署名单位: Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0650-8
• 发表日期: 2016
• 页码: 1-65
• 关键词: integrals

摘要

We use the formalism of Hairer's regularity structures theory to study a heat equation model 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 Hairer [Invent Math 198(2):269-504, (2014)], 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.