Function estimation over the Besov spaces under pointwise ℓr (1 ≤ r < ∞) risks is considered. Minimax rates of convergence are derived using a constrained risk inequality and wavelets. Adaptation ...

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A singularly perturbed quasi-linear two-point boundary value problem with an exponential boundary layer is considered. The problem is discretized using a nonstandard upwinded first-order difference ...

Abstract: We consider algorithms for prediction, compression and entropy estimation in a universal setup. In each case, we estimate some function of an unknown distribution p over the set of natural ...

Modern pointwise ergodic theory developed largely out of the work of Bourgain in the late 80s and early 90s, but recent efforts over the past 10 years have seen the field develop in new directions, as ...