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

TL;DR

This paper investigates the asymptotic behavior of quantization error for a Wiener process starting from a Gaussian distribution, providing initial results and numerical insights into the eigenvalues of its covariance operator.

Contribution

It introduces the first asymptotic results for quantization error in GSP-Wiener processes using classical and analytical methods.

Findings

Initial asymptotic formula for quantization error derived.

Numerical experiments provide insights into eigenvalues of the covariance operator.

Comments on sharp asymptotics based on numerical analysis.

Abstract

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.