Observing that the recent developments of spatial discretization schemes based on recursive (product) quantization can be applied to a wide family of discrete time Markov chains, including all standard time discretization schemes of diffusion processes, we establish in this paper a generic strong error bound for such quantized schemes under a Lipschitz propagation assumption. We also establish a marginal weak error estimate that is entirely new to our best knowledge. As an illustration of their generality, we show how to recursively quantize the Euler scheme of a jump diffusion process, including details on the algorithmic aspects grid computation, transition weight computation, etc. Finally, we test the performances of the recursive quantization algorithm by pricing a European put option in a jump Merton model.

中文翻译：

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递归量化的弱和强误差分析：一种通用方法及其在跳跃扩散中的应用

观察到基于递归（乘积）量化的空间离散化方案的最新发展可以应用于一系列离散时间马尔可夫链，包括扩散过程的所有标准时间离散化方案，我们在本文中建立了一个通用的强误差界Lipschitz传播假设下的这种量化方案。我们还建立了边际弱误差估计，这对我们的最新知识来说是全新的。为了说明它们的一般性，我们展示了如何对跳跃扩散过程的Euler方案进行递归量化，包括有关算法方面的详细信息网格计算，过渡权重计算等。最后，我们通过定价来测试递归量化算法的性能。欧洲看跌期权 跳跃默顿模型中的选项。