Stochastic processes and fractals

Tóm tắt báo cáo

The most known fractals are invariant sets with respect to a system of contraction maps, especially the so called self similar sets.
  Hutchinson and Rüschendorf  gave a simple proof for the existence and uniqueness of invariant random fractal sets and fractal functions using probability metrics defined by expectation.  In these works a finite first moment condition is essential. However, using contraction method in probabilistic metric spaces,
 We can give weaker conditions for the existence and uniqueness of invariant random fractal sets and functions.