Selfsimilar processes with stationary increments in the second Wiener chaos

  1. Makoto Maejima
  2. Ciprian A. Tudor tudor@math.univ-lille1.fr

Abstract

We study average case approximation of Euler and Wiener integrated processes of d variables which are almost surely rk-imes continuously differentiable with respect to the k-th variable and 0 ¬ rk ¬ rk+1. Let n("; d) denote the minimal number of continuous linear functionals which is needed to find an algorithm that uses n such functionals and whose average case error improves the average case error of the zero algorithm by a factor ". We prove that the Wiener process is much more difficult to approximate than the Euler process.

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Probability and Mathematical Statistics

32, z. 1, 2012

Pages from 167 to 186

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