  The characterization of particle diffusion is a classical problem in physics
and probability theory. The field of microrheology is based on experiments in
which microscopic tracer beads are placed into a non-Newtonian fluid and
tracked using high speed video capture. The modeling of the behavior of these
beads is now an active scientific area which demands multiple stochastic and
statistical methods.
  We propose an approximate wavelet-based simulation technique for two classes
of continuous time anomalous diffusion models, the fractional
Ornstein-Uhlenbeck process and the fractional generalized Langevin equation.
The proposed algorithm is an iterative method that provides approximate
discretizations that converge quickly and in an appropriate sense to the
continuous time target process. As compared to previous works, it covers cases
where the natural discretization of the target process does not have closed
form in the time domain. Moreover, we propose smoothing procedures as to speed
the time domain decay of the filters.
