  We study average case approximation of Euler and Wiener integrated processes
of d variables which are almost surely r_k-times continuously differentiable
with respect to the k-th variable. Let n(h,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 h. Strong polynomial tractability means that
there are nonnegative numbers C and p such that n(h,d)< C h^{-p} for all d and
0<h<1.
  We prove that the Wiener process is much more difficult to approximate than
the Euler process. Namely, strong polynomial tractability holds for the Euler
case iff liminf r_k /ln k > 1/(2\ln 3), whereas it holds for the Wiener case
iff liminf r_k/k^s > 0 for some s>1/2. Other types of tractability are also
studied.
