A continuous mapping theorem for the argmin-set functional with applications to convex stochastic processes

Title:

A continuous mapping theorem for the argmin-set functional with applications to convex stochastic processes

Creator:

Ferger, Dietmar

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:de505b61-ddf5-44da-85a7-56e022e88eab
uuid:de505b61-ddf5-44da-85a7-56e022e88eab
doi:10.14736/kyb-2021-3-0426

Subject:

convex stochastic processes, sets of approximating minimizers, weak convergence, Vietoris hyperspace topologies, and Choquet-capacity

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

For lower-semicontinuous and convex stochastic processes Zn and nonnegative random variables ϵn we investigate the pertaining random sets A(Zn,ϵn) of all ϵn-approximating minimizers of Zn. It is shown that, if the finite dimensional distributions of the Zn converge to some Z and if the ϵn converge in probability to some constant c, then the A(Zn,ϵn) converge in distribution to A(Z,c) in the hyperspace of Vietoris. As a simple corollary we obtain an extension of several argmin-theorems in the literature. In particular, in contrast to these argmin-theorems we do not require that the limit process has a unique minimizing point. In the non-unique case the limit-distribution is replaced by a Choquet-capacity.

Language:

English

Rights:

http://creativecommons.org/licenses/by-nc-sa/4.0/
policy:public

Coverage:

426-445

Source:

Kybernetika | 2021 Volume:57 | Number:3

Harvested from:

CDK

Metadata only:

false