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The paper studies the Sample Average Approximation method to solve riskaverse stochastic programs expressed in terms of divergence risk measures. Itcontinues the recent contribution [18] on the first order asymptotics of theoptimal values. We study asymptotic statistical properties of the optimalsolutions, deriving general convergence rates and asymptotic distributions. Asa crucial point the investigations are based on a new type of conditions fromthe theory of empirical processes which do not rely on pathwise analyticalproperties of the goal functions. In particular, continuity in the parameter isnot imposed in advance as usual in the literature on the Sample AverageApproximation method. It is also shown that the new condition is satisfied ifthe paths of the goal functions are Hoelder continuous so that the main resultscarry over in this case. Moreover, the main results are applied to goalfunctions whose paths are piecewise linear as e.g. in two stage mixed-integerprograms.

Asymptotics of solutions of the sample average approximation method to solve risk averse stochastic programs