Random lsc functions: Scalarization
- with Lisa A. Korf, IBM Watson Research Center, Yorktown Heights
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Content:
A random lsc (lower semicontinuous) function is a (measurable) mapping
from a probability space to SCFCNS(X), the space of lsc extended
real-valued functions defined on a metric space X, here is a Polish space.
A
scalarization of a random lsc function f identifies
a countable collection of (extended) real-valued random variables
that uniquely defines f. Given a sequence of random lsc
functions, we bring to the fore a particular class
of scalarizations that inherit the independence, stationarity and ergodicity
properties of the sequence of random lsc functions.
Such scalarizations are exploited in our article
Random lsc
functions: an Ergodic Theorem
and here, to construct an lsc version of
the conditional expectation of a random lsc function.