Geodesic
On the Argmin-sets of stochastic processes and their distributional convergence in Fell-type-topologies
Kybernetika, Tome 47 (2011) no. 6, pp. 955-968 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 49J53, 60B10, 60F05, 90C15
Keywords: $\epsilon$-argmin of stochastic process; random closed sets; weak convergence of Hoffmann--Jørgensen; Fell-topology; Missing-topology 
@article{KYB_2011_47_6_a11,
     author = {Ferger, Dietmar},
     title = {On the {Argmin-sets} of stochastic processes and their distributional convergence in {Fell-type-topologies}},
     journal = {Kybernetika},
     pages = {955--968},
     year = {2011},
     volume = {47},
     number = {6},
     mrnumber = {2907854},
     zbl = {1241.93054},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2011_47_6_a11/}
}
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Ferger, Dietmar. On the Argmin-sets of stochastic processes and their distributional convergence in Fell-type-topologies. Kybernetika, Tome 47 (2011) no. 6, pp. 955-968. http://geodesic.mathdoc.fr/item/KYB_2011_47_6_a11/

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