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High-resolution quantization and entropy coding for fractional Brownian motion. (English) Zbl 1110.60030
Summary: We establish the precise asymptotics of the quantization and entropy coding errors for fractional Brownian motion with respect to the supremum norm and $$L^p [0,1]$$-norm distortions. We show that all moments in the quantization problem lead to the same asymptotics. Using a general principle, we conclude that entropy coding and quantization coincide asymptotically. Under supremum-norm distortion, our proof uses an explicit construction of efficient codebooks based on a particular entropy constrained coding scheme.

##### MSC:
 60G15 Gaussian processes 94A29 Source coding 60G35 Signal detection and filtering (aspects of stochastic processes)
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