On Hausdorff dimension of random fractals

The main purpose of the thesis is to compute the Hausdorff dimension of random fractals in general metric spaces. Such fractals are generated by random recursive constructions with finite “memory”. I study two different random models. Each of these models has the same underlying non-random Cantor type recursive construction, but they introduce random elements at each step quite differently.; In Chapter 2 I study random fractals generated by recursive constructions with independent scale coefficients whose distribution depends on several previous steps. The Hausdorff dimension is computed using a non-random linear operator associated with the construction and some martingale technique.; In Chapter 3 I study random fractals generated by recursive constructions with different, stationary random mechanism. The computation of Hausdorff dimension uses tools of the Ergodic Theory and Statistical Mechanics.