Quasi-Monte Carlo Simulation of Diffusion

Abstract

A particle method adapted to the simulation of diffusion problems is presented. Time is discretized into increments of length Δt. During each time step, the particles are allowed to random walk to any point by taking steps sampled from a Gaussian distribution centered at the current particle position with variance related to the time discretization Δt. Quasi-random samples are used and the particles are relabeled according to their position at each time step. Convergence is proved for the pure initial-value problem in s space dimensions. For some simple demonstration problems, the numerical results indicate that an improvement is achieved over standard random walk simulation.