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High Resolution Quantization and Entropy Coding for Fractional Brownian Motion

   
@article{EJP344,
	author = {Steffen Dereich and Michael Scheutzow},
	title = {High Resolution Quantization and Entropy Coding for Fractional Brownian Motion},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {11},
	year = {2006},
	keywords = {High-resolution quantization; complexity; stochastic process; entropy; distortion rate function},
	abstract = {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.},
	pages = {no. 28, 700-722},
	issn = {1083-6489},
	doi = {10.1214/EJP.v11-344},    
        url = {http://ejp.ejpecp.org/article/view/344}}