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Selfsimilar corrections to the ergodic theorem for the PascalAdic transformation 

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Published in  Stochastics and Dynamics. 2005, vol. 5, no. 1, p. 125  
Abstract  Let T be the Pascaladic transformation. For any measurable function g, we consider the corrections to the ergodic theorem sum_{k=0}^{j1} g(T^k x)  j/l sum_{k=0}^{l1} g(T^k x). When seen as graphs of functions defined on {0,...,l1}, we show for a suitable class of functions g that these quantities, once properly renormalized, converge to (part of) the graph of a selfaffine function. The latter only depends on the ergodic component of x, and is a deformation of the socalled Blancmange function. We also briefly describe the links with a series of works on Conway recursive $10,000 sequence.  
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Citation (ISO format)  JANVRESSE, É., DE LA RUE, T., VELENIK, Yvan. Selfsimilar corrections to the ergodic theorem for the PascalAdic transformation. In: Stochastics and Dynamics, 2005, vol. 5, n° 1, p. 125. doi: 10.1142/S0219493705001250 https://archiveouverte.unige.ch/unige:6383 