Asymptotic for the quantization error for a Wiener process with Gaussian starting point

The asymptotics for quantization error for a Wiener process with Gaussian starting point (GSP-Wiener process) is investigated. Using the classical methodology and some analytical approach a first result is obtained. We provide some further comments on the sharp asymptotic for the quantization error attending to a numerical experiment around the approximate solutions of the eigenvalues related with the covariance operator of the process.