We introduce a theory of non-commutative Lp spaces suitable for non-commutative probability in a non-tracial setting and use it to develop stochastic analysis of Grassmann-valued processes, including martingale inequalities, stochastic integrals with respect to Grassmann Itô processes, Girsanov’s formula and a weak formulation of Grassmann SDEs. We apply this new setting to the construction of several unbounded random variables, including a Grassmann analog of the φ24 Euclidean QFT in a bounded region.
The talk is based on a joint work with Luca Fresta, Maria Gordina and Massimiliano Gubinelli.
This video was produced by the University of Münster, as part of the workshop Stochastic Analysis meets QFT – critical theory.
