International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 52, Pages 3299-3313
doi:10.1155/S0161171203301048
Self-similar random fractal measures using contraction method in probabilistic metric spaces
József Kolumbán
, Anna Soós
and Ibolya Varga
Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca 3400, Romania
Abstract
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.