an:02228216
Zbl 1082.90552
Korf, Lisa A.; Wets, Roger J.-B.
Random-lsc functions: an ergodic theorem
EN
Math. Oper. Res. 26, No. 2, 421-445 (2001).
00081772
2001
j
90C15 62L20
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
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.