Spatial correlations and variance reduction in Brownian simulations.
Brownian simulation methods have become very popular in the context of complex
fluids since the 1990's. We start with a motivational background to polymeric fluid models
and introduce the notions of Hilbert space-valued Brownian motions and spatial correlation operators.
We then give a general formulation for Brownian simulation methods which differ in different choices of noise correlation.
We present a variance minimization problem in Brownian simulations with respect to an optimal choice of noise correlations.