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On continuous convergence and epi-convergence of random functions. II: Sufficient conditions and applications. (English) Zbl 1249.90185
Summary: Part II of the paper (for part I, see [the authors, ibid. 39, No. 1, 75–98 (2003; Zbl 1249.90184)]) aims at providing conditions which may serve as a bridge between existing stability assertions and asymptotic results in probability theory and statistics. Special emphasis is put on functions that are expectations with respect to random probability measures. Discontinuous integrands are also taken into account. The results are illustrated applying them to functions that represent probabilities.

MSC:
90C15 Stochastic programming
60B10 Convergence of probability measures
62G05 Nonparametric estimation
90C31 Sensitivity, stability, parametric optimization
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