New Algorithms And Fast Implementations To Approximate Stochastic Processes

Understand

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.