  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.
