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

Dietmar Ferger

Kybernetika (2011)

  • Volume: 47, Issue: 6, page 955-968
  • ISSN: 0023-5954

Abstract

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Let ϵ - ( 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 ( Z n ) of such stochastic processes and ( ϵ n ) of nonnegative random variables we give sufficient conditions for the (closed) random sets ϵ n - ( Z n ) to converge in distribution with respect to the Fell-topology and to the coarser Missing-topology.

How to cite

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Ferger, Dietmar. "On the Argmin-sets of stochastic processes and their distributional convergence in Fell-type-topologies." Kybernetika 47.6 (2011): 955-968. <http://eudml.org/doc/196322>.

@article{Ferger2011,
abstract = {Let $\epsilon -\text\{(\}Z)$ 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 $\epsilon _n-\text\{(\}Z_n)$ to converge in distribution with respect to the Fell-topology and to the coarser Missing-topology.},
author = {Ferger, Dietmar},
journal = {Kybernetika},
keywords = {$\epsilon $-argmin of stochastic process; random closed sets; weak convergence of Hoffmann–Jørgensen; Fell-topology; Missing-topology; argmin of stochastic process; random closed sets; weak convergence of Hoffmann-Jørgensen; Fell-topology; missing-topology},
language = {eng},
number = {6},
pages = {955-968},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the Argmin-sets of stochastic processes and their distributional convergence in Fell-type-topologies},
url = {http://eudml.org/doc/196322},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Ferger, Dietmar
TI - On the Argmin-sets of stochastic processes and their distributional convergence in Fell-type-topologies
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 6
SP - 955
EP - 968
AB - Let $\epsilon -\text{(}Z)$ 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 $\epsilon _n-\text{(}Z_n)$ to converge in distribution with respect to the Fell-topology and to the coarser Missing-topology.
LA - eng
KW - $\epsilon $-argmin of stochastic process; random closed sets; weak convergence of Hoffmann–Jørgensen; Fell-topology; Missing-topology; argmin of stochastic process; random closed sets; weak convergence of Hoffmann-Jørgensen; Fell-topology; missing-topology
UR - http://eudml.org/doc/196322
ER -

References

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