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We consider a sequence of empirical stochastic programs with increasing sample size. By mimicking a method of LeCam, we rewrite the program in local coordinates and identify a limiting "asymptotic stochastic program". The objective of this limiting program is typically a sum of a regularly varying function and an indefinitely divisible stochastic process. In particular, the Gaussian shift process, the Wiener process and the Poisson
process are candidates for such asymptotic processes. Examples for these limiting situations are given and the limiting distribution of the minimum value and the minimizer are discussed. It turns out, that asymptotic normality appears only as an important, but special case, other types of limiting distributions appear in a natural way.
