Description: The theory of random dynamical systems originated from stochastic differential It is intended to provide a framework and techniques to describe and analyze the evolution of dynamical systems when the input and output data are known only approximately, according to some probability The development of this field, in both the theory and applications, has gone in many In this manuscript we introduce measurable expanding random dynamical systems, develop the thermodynamical formalism and establish, in particular, the exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not This theory is then used to investigate fractal properties of conformal random We prove a Bowen’s formula and develop the multifractal formalism of the Gibbs Depending on the behavior of the Birkhoff sums of the pressure function we arrive at a natural classification of the systems into two classes: quasi-deterministic systems, which share many properties of deterministic ones; and essentially ra...

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