Korf, Lisa A.; Wets, Roger J.-B. Random-lsc functions: an ergodic theorem. (English) Zbl 1082.90552 Math. Oper. Res. 26, No. 2, 421-445 (2001). 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. Cited in 12 Documents MSC: 90C15 Stochastic programming 62L20 Stochastic approximation Keywords:Stationary processes; ergodic theorem; epi-convergence; Kolmogorov’s extension theorem; stochastic optimization; Bayesian decision theory; composite materials; stochastic programming; random lower semicontinuous functions; random samples PDF BibTeX XML Cite \textit{L. A. Korf} and \textit{R. J. B. Wets}, Math. Oper. Res. 26, No. 2, 421--445 (2001; Zbl 1082.90552) Full Text: DOI