Fractional Brownian Motion and Malliavin-Stein Approach (FraMStA)

The project at a glance

Start date:

01 Sep 2023
Duration in months:

36
Funding:

FNR
Principal Investigator(s):

Ivan NOURDIN

About

In 2009, the PI and G. Peccati introduced a method, typically referred to as Malliavin-Stein (M-S) approach, which combined for the first time Stein’s method with infinite-dimensional integration by parts formulae based on the use of Malliavin-type operators. Since then, this theory has never ceased to grow and has reached today the status of an essential tool of modern stochastic calculus, with regular additions and diverse applications well beyond the context in which it was initially introduced (Gaussian space). Since several years, the mathematics department of the University of Luxembourg has been a major player in the development of the M-S approach. One of our ambition with FraMStA is to further establish our position of global leaders in this domain. The rapid development of the M-S approach was facilitated by the fact that it applied particularly well to the derivation of limit theorems for nonlinear functionals of the fractional Brownian motion (fBm). The study of this process, which is a genuine extension of the standard Brownian motion, poses many challenges, related in particular to the fact that fBm is neither Markovian nor a semimartingale. Nowadays, fBm plays a major driving role in the development of the M-S approach, similar to the crucial place it occupies in the theory of rough paths, which is in turn tightly connected to Martin Hairer’s Fields Medal (2014). The main goal of FraMStA is to further advance the development of the M-S approach and the analysis of fBm in non-standard situations, using tools from stochastic analysis, convex geometry, differential geometry and stochastic analysis.