Czasopisma Naukowe w Sieci (CNS)

Selfsimilar processes with stationary increments in the second Wiener chaos

  1. Makoto Maejima
  2. C. A. Tudor

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

Strony od 167 do 186

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