Random-lsc functions: an ergodic theorem. (English) Zbl 1082.90552

Korf, Lisa A.; Wets, Roger J.-B.

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.

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