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).

Multifractal analysis of sums of random pulses

“…See also [3] for the box dimension of G , or [43,45] for a more systematic study of graph dimensions. When α < h, almost surely dim…”

“…Calling the graph of the process G and its box-dimension, they showed that as soon as there exists an interval I on which (the space of global Hölder real functions of exponent H ) and is -diffeomorphic on some interval, then almost surely See also [ 3 ] for the box dimension of , or [ 43, 45 ] for a more systematic study of graph dimensions. When , almost surely .…”