We derive a high-resolution formula for the quantization and entropy coding approximation quantities for fractional Brownian motion, respective to the supre-mum norm and L p [0, 1]-norm distortions. We show that all moments in the quanti-zation problem lead to the same asymptotics. Using a general principle, we conclude that entropy coding and quantization coincide asymptotically. Under supremu...

We prove that for a so-called sticky process S there exists an equivalent probability Q and a Q-martingale S̃ that is arbitrarily close to S in L(Q) norm. For continuous S, S̃ can be chosen arbitrarily close to S in supremum norm. In the case where S is a local martingale we may choose Q arbitrarily close to the original probability in the total variation norm. We provide examples to illustrate t...

The multivariate integer Chebyshev problem is to find polynomials with integer coefficients that minimize the supremum norm over a compact set in C. We study this problem on general sets, but devote special attention to product sets such as cube and polydisk. We also establish a multivariate analog of the Hilbert-Fekete upper bound for the integer Chebyshev constant, which depends on the dimens...