  We prove that certain asymptotic moments exist for some random distance
expanding dynamical systems and Markov chains in random dynamical environment,
and compute them in terms of the derivatives at the $0$ of an appropriate
pressure function. It will follow that these moments satisfy the relations that
the asymptotic moments $\gam_k=\lim_{n\to\infty}n^{-[\frac
k2]}\bbE(\sum_{i=1}^n X_i)^k$ of sums of independent and identically
distributed random variables satisfy. We will also obtain certain (Edgeworth)
asymptotic expansions related to the central limit theorem for such processes.
Our proofs rely on a (parametric) random complex Ruelle-Perron-Frobenius
theorem, which replaces some the spectral techniques which are used in
literature in order to obtain limit theorems for deterministic dynamical
systems and Markov chains.
