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

Publikation: Beitrag in Fachzeitschrift › Forschungsartikel › Beigetragen › Begutachtung

Beitragende

Abstract

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.

Details

OriginalspracheEnglisch
Seiten (von - bis)426-445
Seitenumfang20
FachzeitschriftKybernetika
Jahrgang57
Ausgabenummer3
PublikationsstatusVeröffentlicht - 2021
Peer-Review-StatusJa

Schlagworte

ASJC Scopus Sachgebiete

  • Software - Choquet-capacity, Convex stochastic processes, Sets of approximating minimizers, Vietoris hyperspace topologies, Weak convergence
  • Steuerungs- und Systemtechnik - Choquet-capacity, Convex stochastic processes, Sets of approximating minimizers, Vietoris hyperspace topologies, Weak convergence
  • Theoretische Informatik - Choquet-capacity, Convex stochastic processes, Sets of approximating minimizers, Vietoris hyperspace topologies, Weak convergence
  • Information systems - Choquet-capacity, Convex stochastic processes, Sets of approximating minimizers, Vietoris hyperspace topologies, Weak convergence
  • Artificial intelligence - Choquet-capacity, Convex stochastic processes, Sets of approximating minimizers, Vietoris hyperspace topologies, Weak convergence
  • Elektrotechnik und Elektronik - Choquet-capacity, Convex stochastic processes, Sets of approximating minimizers, Vietoris hyperspace topologies, Weak convergence

Schlagwörter

  • Choquet-capacity, Convex stochastic processes, Sets of approximating minimizers, Vietoris hyperspace topologies, Weak convergence

Bibliotheksschlagworte

  • 510 Mathematik - Choquet-capacity, Convex stochastic processes, Sets of approximating minimizers, Vietoris hyperspace topologies, Weak convergence