Recently it was shown [W. Koch, F Grossmann, J.T. Stockburger, J. Ankerhold, Phys. Rev. Lett. 100 (2008) 230402] that a combination of an exact stochastic decomposition of non-Markovian dissipative quantum dynamics with the time-dependent semiclassical initial value formalism offers a powerful tool to describe quantum Brownian motion in domains of parameter space where other approaches fail. In particular, low temperatures, stronger friction, a wide range of spectral bath densities, and continuous nonlinear systems can be treated. Details of this formulation including its numerical implementation and the impact of non-Markovian phenomena are discussed for the exactly solvable case of a harmonic oscillator. (C) 2009 Elsevier B.V. All rights reserved.