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

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  • Dereich, Steffen

Abstract

We investigate the high resolution quantization and entropy coding problem for solutions of stochastic differential equations under Lp[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.

Suggested Citation

  • Dereich, Steffen, 2008. "The coding complexity of diffusion processes under Lp[0,1]-norm distortion," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 938-951, June.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:6:p:938-951
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    References listed on IDEAS

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    1. Luschgy, Harald & Pagès, Gilles, 2006. "Functional quantization of a class of Brownian diffusions: A constructive approach," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 310-336, February.
    2. Dereich, Steffen, 2008. "The coding complexity of diffusion processes under supremum norm distortion," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 917-937, June.
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