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Stochastic approximations and differential inclusions

Auteur(s)
Benaim, Michel 
Institut de mathématiques 
Hofbauer, Josef
Sorin, Sylvain
Date de parution
2005
In
Siam Journal on Control and Optimization
Vol.
1
No
44
De la page
328
A la page
348
Mots-clés
  • stochastic approximation
  • differential inclusions
  • set-valued dynamical
  • systems
  • chain recurrence
  • approachability
  • game theory
  • learning
  • fictitious play
  • FICTITIOUS PLAY
  • DYNAMICAL-SYSTEMS
  • GAMES
  • CONVERGENCE
  • ALGORITHMS
  • stochastic approximat...

  • differential inclusio...

  • set-valued dynamical

  • systems

  • chain recurrence

  • approachability

  • game theory

  • learning

  • fictitious play

  • FICTITIOUS PLAY

  • DYNAMICAL-SYSTEMS

  • GAMES

  • CONVERGENCE

  • ALGORITHMS

Résumé
The dynamical systems approach to stochastic approximation is generalized to the case where the mean differential equation is replaced by a differential inclusion. The limit set theorem of Benaim and Hirsch is extended to this situation. Internally chain transitive sets and attractors are studied in detail for set-valued dynamical systems. Applications to game theory are given, in particular to Blackwell's approachability theorem and the convergence of fictitious play.
Identifiants
https://libra.unine.ch/handle/123456789/6246
_
10.1137/S0363012904439301
Type de publication
journal article
Dossier(s) à télécharger
 main article: document (2).pdf (522.24 KB)
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