New Algorithms And Fast Implementations To Approximate Stochastic Processes
This work addresses the problem of efficiently approximating stochastic processes for numerical computations, which is crucial for researchers and practitioners working with stochastic models.
This paper introduces new algorithms and fast implementations for approximating stochastic processes. The goal is to develop finite models that accurately represent real data processes, with different estimation methods depending on whether the stochastic model is known, a simulation algorithm is available, or only observed trajectories are provided.
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.