论文标题
新算法和快速实现以近似随机过程
New Algorithms And Fast Implementations To Approximate Stochastic Processes
论文作者
论文摘要
我们提出了新的算法和快速实现，以找到建模随机过程的有效近似值。对于许多数值计算，必须为随机过程开发有限的近似值。虽然目标始终是找到一个有限模型，该模型代表了有关真实数据过程的给定知识，但估算离散近似模型的方法可能会大不相同：（i）如果随机模型被称为随机差分方程的解决方案，例如，例如，一个人可能会直接从指定模型中产生场景； （ii）如果有一个模拟算法可用，该算法允许从所有条件分布中模拟轨迹，则可以通过随机近似来生成场景树； （iii）如果仅可用一些观察到的场景过程轨迹，则近似过程的构建可以基于非参数条件密度估计。
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.
