Rate of convergence for Hilbert space valued processes

Moritz Jirak

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arXiv · 1707.09637

Rate of convergence for Hilbert space valued processes

Moritz Jirak

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Abstract

Consider a stationary, linear Hilbert space valued process. We establish Berry-Essen type results with optimal convergence rates under sharp dependence conditions on the underlying coefficient sequence of the linear operators. The case of non-linear Bernoulli-shift sequences is also considered. If the sequence is $m$-dependent, the optimal rate $(n/m)^{1/2}$ is reached. If the sequence is weakly geometrically dependent, the rate $(n/\log n)^{1/2}$ is obtained.

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BibTeX RIS

Moritz Jirak. 2017-07-30. Rate of convergence for Hilbert space valued processes. https://arxiv.org/abs/1707.09637

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