We establish upper bounds for the $L^p$-quantization error, p in (1, 2+d), induced by the recursive Markovian quantization of a d-dimensional diffusion discretized via the Euler scheme. We introduce a hybrid recursive quantization scheme, easier to implement in the high-dimensional framework, and establish upper bounds to the corresponding $L^p$-quantization error. To take advantage of these extensions, we propose a time discretization scheme and a recursive quantization-based discretization scheme associated to a reflected Backward Stochastic Differential Equation and estimate $L^p$-error bounds induced by the space approximation. We will explain how to numerically compute the solution of the reflected BSDE relying on the recursive quantization and compare it to other types of quantization.

翻译：我们为$L ⁇ p$-量化错误设定了上限, p in (1, 2+d),这是由通过 Euler 方案分离的二维扩散的递回式 Markovian 量化法引发的。 我们引入了混合递回量化办法, 更容易在高维框架内实施, 并且为相应的 $L ⁇ p$-量化错误设定上限。 为了利用这些扩展, 我们提议了一个时间分解办法和基于递回量化的离异办法, 与空间近似所引发的反反向托盘差异和估计 $L ⁇ p$- error 界限相关联。 我们将解释如何用数字计算反射 BSDE 的解决方案, 依赖递回式量化, 并将其与其他类型的量化比较 。