Kybernetika 47 no. 6, 955-968, 2011

On the argmin-sets of stochastic processes and their distributional convergence in Fell-type-topologies

Dietmar Ferger


Let <span class="tex">&epsilon;</span>-Argmin<span class="tex">(Z)</span> be the collection of all <span class="tex">&epsilon;</span>-optimal solutions for a stochastic process <span class="tex">Z</span> with locally bounded trajectories defined on a topological space. For sequences <span class="tex">(Z<sub>n</sub>)</span> of such stochastic processes and <span class="tex">(&epsilon;<sub>n</sub>)</span> of nonnegative random variables we give sufficient conditions for the (closed) random sets <span class="tex">&epsilon;<sub>n</sub></span>-Argmin<span class="tex">(Z<sub>n</sub>)</span> 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


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