PDE seminar by Fabian Andsem Harang
Speaker: Fabian Andsem Harang (UiO)
Title: Integration with respect to Rough Hölder Fields
Abstract: In this talk we will propose a generalization of the theory of rough paths to rough fields. By rough fields we mean multi-variable functions with values in R with some Hölder type regularity in each variable. Typical examples of this would be a (fractional) Brownian sheet, or other Gaussian random fields. We will discuss the construction of an integral with respect to such fields, and find a suitable class of integrands. At last we will show applications to (non-linear) hyperbolic equations driven by a possibly rough space-time noise.