The coding complexity of diffusion processes under Lp[0, 1]-norm distortion

TitleThe coding complexity of diffusion processes under Lp[0, 1]-norm distortion
Publication TypeJournal Article
Year of Publication2008
AuthorsSteffen Dereich
JournalStochastic Processes and their Applications
Volume118
Issue6
Pagination938-951
Date PublishedJune
Keywordscomplexity, High-resolution quantization, stochastic differential equations, stochastic processes
Abstract

We investigate the high resolution quantization and entropy coding problem for solutions of stochastic differential equations under $ L^p[0, 1] $-norm distortion. We find explicit high resolution formulas in terms of the average diffusion coefficient seen by the process. The proof is based on a decoupling method introduced in a former article by the author. Given that link it remains to analyze the coding problem for a concatenation of Wiener processes and to solve the corresponding rate allocation problem.