Let ε-Argmin(Z) be the collection of all ε-optimal solutions for a stochastic process Z with locally bounded trajectories defined on a topological space. For sequences (Zn) of such stochastic processes and (εn) of nonnegative random variables we give sufficient conditions for the (closed) random sets εn-Argmin(Zn) to converge in distribution with respect to the Fell-topology and to the coarser Missing-topology.
$\epsilon -$argmin of stochastic process, random closed sets, weak convergence of Hoffmann-Jørgensen, Fell-topology, Missing-topology
49J53, 60B10, 60F05, 90C15