Wavelet construction of quantum Brownian motions and bridges

David Applebaum, University of Sheffield

I'll introduce "probabilistic" and "stochastic Hilbertian structures". These seem to be a suitable context for developing a theory of "quantum Gaussian processes". The Schauder system will be utilised to give a wavelet representation of quantum Brownian motion as operators in Fock space over a space of square summable sequences. Quantum Brownian bridges will be defined and a number of representations of these will be given.