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Self-similar corrections to the ergodic theorem for the Pascal-Adic transformation

Janvresse, É.
de la Rue, T.
Published in Stochastics and dynamics. 2005, vol. 5, no. 1, p. 1-25
Abstract Let T be the Pascal-adic transformation. For any measurable function g, we consider the corrections to the ergodic theorem sum_{k=0}^{j-1} g(T^k x) - j/l sum_{k=0}^{l-1} g(T^k x). When seen as graphs of functions defined on {0,...,l-1}, we show for a suitable class of functions g that these quantities, once properly renormalized, converge to (part of) the graph of a self-affine function. The latter only depends on the ergodic component of x, and is a deformation of the so-called Blancmange function. We also briefly describe the links with a series of works on Conway recursive $10,000 sequence.
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JANVRESSE, É., DE LA RUE, T., VELENIK, Yvan. Self-similar corrections to the ergodic theorem for the Pascal-Adic transformation. In: Stochastics and dynamics, 2005, vol. 5, n° 1, p. 1-25. doi: 10.1142/S0219493705001250

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Deposited on : 2010-04-27

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