Grey Brownian motion was introduced by Schneider in 1990. In his work Schneider showed that indeed the process fulfills a Feynman-Kac like formula for the solution of the fractional heat equation. In the 2000s the process was generalized by Mainardi et al. In 2016 the group of Grothaus established a White Noise like calculus for the process, also introducing spaces of test and generalized functions.
In this talk, we will review this recent development and give an overview of the analysis and the most recent results. In an outlook, we give a strategy on how to introduce spaces of regular distributions to obtain a form of regularity theory.
Best regards, L.