  Observing that the recent developments of the recursive (product)
quantization method induces a family of Markov chains which includes all
standard discretization schemes of diffusions processes , we propose to compute
a general error bound induced by the recursive quantization schemes using this
generic markovian structure. Furthermore, we compute a marginal weak error for
the recursive quantization. We also extend the recursive quantization method to
the Euler scheme associated to diffusion processes with jumps, which still have
this markovian structure, and we say how to compute the recursive quantization
and the associated weights and transition weights.
