Random LSC Functions: An Ergodic Theorem

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 material...

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Bibliographic Details
Published in:Mathematics of operations research 2001-05, Vol.26 (2), p.421-445
Main Authors: Korf, Lisa A, Wets, Roger J.-B
Format: Article
Language:English
Subjects:
Bayesian analysis
Bayesian decision theory
composite materials
Decision theory
epi-convergence
ergodic theorem
Ergodic theory
Homogenization
Kolmogorov extension
Kolmogorov's extension theorem
Mathematical functions
Probabilities
random lower semicontinuous functions
random samples
Random variables
Scalability
Stationary processes
Stochastic models
stochastic optimization
stochastic programming
Studies
Topological spaces
Topological theorems
Topology
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Description
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.
ISSN:0364-765X
1526-5471
DOI:10.1287/moor.26.2.421.10548