Christian Bender: Discretizing Malliavin calculus
Christian Bender (Saarland University) gives a lecture with the title: Discretizing Malliavin calculus
Suppose B is a Brownian motion and B^n is an approximating sequence of rescaled random walks on the same probability space converging to B pointwise in probability. Based on the discrete-time noise one can define discrete-time analogues of some basic operators of Malliavin calculus such as the chaos decomposition, the Malliavin derivative, and the Skorokhod integral. In this talk, we discuss several convergence results for these discretized operators to their continuous counterparts in the weak and strong L^2-topology, and, in particular, explain why these results hold independently of the discrete-time noise distribution. This is a joint work with Peter Parczewski (Mannheim).