The coding complexity of diffusion processes under \(L^p[0,1]\)-norm distortion
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.
scientific article; zbMATH DE number 5285977
scientific article