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.

翻译：我们提出了新的算法和快速实施方法,以找到用于模拟随机过程的高效近似值。对于许多数字计算来说,有必要为随机过程开发有限的近近似值。虽然目标总是要找到一个有限的模型,这代表了对真实数据过程的尽可能准确的一定了解,但估计离散近似模型的方法可能大不相同:(一) 如果随机模型被称为随机差分方程的解决方案,例如,人们可以直接从指定的模型中生成假想树;(二) 如果存在模拟算法,可以模拟所有有条件分布的轨迹,那么假设树可以由随机近似生成;(三) 如果只有所观测到的假想过程的轨迹,则根据非参数性密度估计来构建近似进程。