The coding complexity of diffusion processes under \(L^p[0,1]\)-norm distortion
type: Item
instance of: scholarly article
title: The coding complexity of diffusion processes under \(L^p[0,1]\)-norm distortion
zbMATH Open document ID: 1151.60018
author: Steffen Dereich
published in: Stochastic Processes and their Applications
publication date: 2008-06-10T00:00:00Z
review text: The paper treates the high resolution quantization and entropy coding problem for \(1\)-dimensional diffusions \(X\) under \(L^p[0,1]\)-norm. The original process \(X\) is an adapted semimartingale solving the integral equaton with non-homogeneous coefficients, and it is approximated by some reconstruction. The quantization error, entropy coding error and the distortion rate function are introduced and analyzed. The main result is the explicit high resolution formula for diffusion that is established in terms of the average diffusion coefficient. At the beginning, the asymptotic coding problem for the Wiener process is considered and then one of the results relates the coding problem for the diffusion to that of a concatenation of Wiener processes. The proofs are based on a decoupling argument in order to analyze the supremum norm distortion setting.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 94A15
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 5285977
zbMATH Keywords: high-resolution quantization
zbMATH Keywords: complexity
zbMATH Keywords: stochastic processes
zbMATH Keywords: stochastic differential equations
MaRDI profile type: Publication
full work available at URL: j.spa.2007.07.002
OpenAlex ID: W4213069834
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DOI: 10.1016/J.SPA.2007.07.002
description: scientific article; zbMATH DE number 5285977