1. On the Argmin-sets of stochastic processes and their distributional convergence in Fell-type-topologies
- Creator:
- Ferger, Dietmar
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- ϵ-Argmin of stochastic process, random closed sets, weak convergence of Hoffmann-Jørgensen, Fell-topology, and Missing-topology
- Language:
- English
- Description:
- Let <span class="tex">ε</span>-Argmin<span class="tex">(Z)</span> be the collection of all <span class="tex">ε</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">(ε<sub>n</sub>)</span> of nonnegative random variables we give sufficient conditions for the (closed) random sets <span class="tex">ε<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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public