Central Limit Theorems for the Brownian motion on large unitary groups

Key words: H¨ older continuity, fractional Brownian motion, Skorohod integrals, Gaussian sobolev spaces, rough path, distributions.. AMS Subject classification (2000): 60G15,

It is a unitary operator-valued L´evy process with re- spect to the free multiplicative convolution of probability measures on the unit circle T (or equivalently the multiplication

The classical scaled path properties of branching Brownian motion (BBM) have now been well-studied: for ex- ample, see Lee [13] and Hardy and Harris [3] for large deviation results

This is to say, we get an expression for the Itô excursion measure of the reflected Langevin process as a limit of known measures.. This result resembles the classical approximation

As a by-product, geometric rough paths associated to elements of the reproducing kernel Hilbert space of the fractional Brownian motion are obtained and an explicit

Examples of fractal sets, for which an average density of order three can be defined using a density gauge function different from the exponential type ϕ(r) = r α are the path of

We focus here on results of Berestycki, Berestycki and Schweinsberg [5] concerning the branching Brownian motion in a strip, where particles move according to a Brownian motion

The linear Boltzmann equation has been derived (globally in time) from the dynamics of a tagged particle in a low density Lorentz gas, meaning that.. • the obstacles are