Pathwise Gaussian Volterra processes in Hilbert space
We discuss a rough volatility model with fractional drift and noise allowing for more flexibility in modelling roughness. Motivated by an extension to infinite stochastic volatility models for commodity futures markets, we are led to a study of Gaussian Volterra processes. We suggest a definition of a pathwise stochastic integral based on combining the regularity of the kernel and the covariance of the noise. Likewise, we define pathwise integration with respect to multi-parameter covariance-like functions, and apply this to derive an explicit representation of the covariance of the Gaussian Volterra process. This is joint work with Fabian Harang (Oslo).