Optimal choices of correlation operators in brownian simulation methods

We analyze Brownian simulation methods for systems of partial differential equations coupled to convection-diffusion equations. In many situations the spatial correlation of Brownian noise can be viewed as a free parameter. We formulate the choice of the noise correlation as an optimization problem for mean error minimization. In contrast to earlier work which was restricted to systems of finite dimensions, our formulation is performed in function space. We then provide an approximation theorem that reduces the problem into the solution of finite-dimensional semidefinite programming problems. Examples are given to illustrate our main results.