  Quantization for probability distributions refers broadly to estimating a
given probability measure by a discrete probability measure supported by a
finite number of points. We consider general geometric approaches to
quantization using stationary processes arising in dynamical systems, followed
by a discussion of the special cases of stationary processes: random processes
and Diophantine processes. We are interested in how close stationary process
can be to giving optimal $n$-means and $n^{th}$ optimal mean distortion errors.
We also consider different ways of measuring the degree of approximation by
quantization, and their advantages and disadvantages in these different
contexts.
