Self‐similar random fractal measures using contraction method in probabilistic metric spaces

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.