International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 52, Pages 3299-3313
Self-similar random fractal measures using contraction method in probabilistic metric spaces
Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca 3400, Romania
Received 2 January 2003
Copyright © 2003 József Kolumbán et al. 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.
Self-similar random fractal measures were studied by Hutchinson
and Rüschendorf. Working with probability metric in complete
metric spaces, they need the first moment condition for the
existence and uniqueness of these measures. In this paper, we use contraction
method in probabilistic metric spaces to prove the existence and
uniqueness of self-similar random fractal measures replacing the
first moment condition.