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On the argmin-sets of stochastic processes and their distributional convergence in Fell-type-topologies. (English) Zbl 1241.93054
Summary: Let \(\epsilon-\)Argmin(Z) be the collection of all \(\epsilon \)-optimal solutions for a stochastic process Z with locally bounded trajectories defined on a topological space. For sequences \((Z_{n})\) of such stochastic processes and \((\epsilon _{n})\) of nonnegative random variables we give sufficient conditions for the (closed) random sets \(\epsilon _{n}-\)Argmin\((Z_{n})\) to converge in distribution with respect to the Fell-topology and to the coarser Missing-topology.

MSC:
93E20 Optimal stochastic control
49J53 Set-valued and variational analysis
60B10 Convergence of probability measures
60F05 Central limit and other weak theorems
90C15 Stochastic programming
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