The quantization complexity of diffusion processes

TL;DR

This paper studies the complexity of quantizing solutions to stochastic differential equations in function spaces, providing asymptotic estimates and a decoupling method relating diffusion process complexity to Wiener processes.

Contribution

It introduces a decoupling technique to analyze the quantization complexity of diffusion processes under weak regularity assumptions.

Findings

Derived tight asymptotic estimates for high resolution coding of diffusion solutions.

Established a relation between diffusion process complexity and Wiener process complexity.

Provided a novel decoupling method for analyzing stochastic differential equations.

Abstract

We investigate the high resolution coding problem for solutions of stochastic differential equations in the L^p[0,1]- and the C[0,1]-space. Tight asymptotic estimates are found under weak regularity assumptions. The main technical tool is a decoupling method which allows us to relate the complexity of the diffusion process to that of the Wiener process under certain random distortions.