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Random-lsc functions: an ergodic theorem. (English) Zbl 1082.90552
Summary: An ergodic theorem for random lsc (lower semicontinuous) functions is obtained by relying on a “scalarization” of such functions. In the process, Kolmogorov’s extension theorem for random lsc functions is established. Applications to statistical estimation problems, composite materials, and stochastic optimization problems are briefly noted.

MSC:
90C15 Stochastic programming
62L20 Stochastic approximation
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