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

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 sufficient...

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Bibliographic Details
Published in:Rendiconti del Circolo matematico di Palermo 2011-12, Vol.60 (3), p.469-476
Main Authors: de Amo, Enrique, Bhouri, Imen, Fernández-Sánchez, Juan
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
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Summary: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 ).
ISSN:0009-725X
1973-4409
DOI:10.1007/s12215-011-0061-3