A note on the Hausdorff dimension of general sums of pulses graphs

Abstract

In this work we study the some general fractal sums of pulses defined in ℝ by: where (a n), (λ n) two positive scalar sequences such that ∑a n is divergent, and (λ n) is non-increasing to 0, G is an elementary bump and X n are independent random variables uniformly distributed on a sufficiently large domain Ω. We investigate the Hausdorff dimension of the graph of G and in particular we answer a question given by Tricot in (Courbes et dimensions fractales, Springer, Berlin, 1995). © 2011 The Author(s).