Self-similar random fractal measures using contraction method in probabilistic metric spacesReport as inadecuate




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International Journal of Mathematics and Mathematical Sciences - Volume 2003 2003, Issue 52, Pages 3299-3313

Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca 3400, Romania

Received 2 January 2003

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Self-similar random fractal measures were studied by Hutchinsonand Rüschendorf. Working with probability metric in completemetric spaces, they need the first moment condition for theexistence and uniqueness of these measures. In this paper, we use contractionmethod in probabilistic metric spaces to prove the existence anduniqueness of self-similar random fractal measures replacing thefirst moment condition.





Author: József Kolumbán, Anna Soós, and Ibolya Varga

Source: https://www.hindawi.com/



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