  We present new algorithms and fast implementations to find efficient
approximations for modelling stochastic processes. For many numerical
computations it is essential to develop finite approximations for stochastic
processes. While the goal is always to find a finite model, which represents a
given knowledge about the real data process as accurate as possible, the ways
of estimating the discrete approximating model may be quite different: (i) if
the stochastic model is known as a solution of a stochastic differential
equation, e.g., one may generate the scenario tree directly from the specified
model; (ii) if a simulation algorithm is available, which allows simulating
trajectories from all conditional distributions, a scenario tree can be
generated by stochastic approximation; (iii) if only some observed trajectories
of the scenario process are available, the construction of the approximating
process can be based on non-parametric conditional density estimates.
