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Let be the polygonal partial sums processes built
on the linear processes ,
n ≥ 1, where are
i.i.d., centered random elements in some
separable Hilbert space and the ai's are bounded linear
operators , with . We
investigate functional central limit theorem for in the
Hölder spaces of functions
such that ||x(t + h) - x(t)|| = o(p(h))
uniformly in t, where p(h) = hαL(1/h), 0 ≤ h ≤ 1
with 0 ≤ α ≤ 1/2 and L slowly varying at infinity. We
obtain the weak convergence of ...
This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims to give a macroscopic approximation that takes into account the microscopic heterogeneities. This paper follows [Probab. Theory Related Fields (2009)] and improves this latter work by...
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