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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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