Rates in the strong invariance principle for ergodic automorphisms of the torus
Keyword(s):
Let T be an ergodic automorphism of the d-dimensional torus 𝕋d. In the spirit of Le Borgne, we give conditions on the Fourier coefficients of a function f from 𝕋d to ℝ under which the partial sums f ◦ T + f ◦ T2 + ⋯ + f ◦ Tn satisfy a strong invariance principle. Next, reinforcing the condition on the Fourier coefficients in a natural way, we obtain explicit rates of convergence in the strong invariance principle, up to n1/4 log n.
Keyword(s):
2013 ◽
Vol 157
(1-2)
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pp. 509-509
1986 ◽
Vol 30
(1)
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pp. 148-152
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2011 ◽
Vol 61
(1)
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pp. 27-40
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2001 ◽
Vol 93
(2)
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pp. 317-337
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Keyword(s):
2005 ◽
Vol 33
(2)
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pp. 823-840
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