A Local Refinement Strategy for Constructive Quantization of Scalar SDEs

We present a fully constructive method for quantization of the solution X of a scalar SDE in the path space L _p 0,1] or C0,1]. The construction relies on a refinement strategy which takes into account the local regularity of X and uses Brownian motion (bridge) quantization as a building block. Our algorithm is easy to implement, its computational cost is close to the size of the quantization, and it achieves strong asymptotic optimality provided this property holds for the Brownian motion (bridge) quantization.