Skip to Main content Skip to Navigation
Journal articles

Stochastic approximations of set-valued dynamical systems: Convergence with positive probability to an attractor

Mathieu Faure 1, * Gregory Roth 1, *
* Corresponding author
Abstract : A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition, convergence to a given attractor of the flow induced by this dynamical system was proved to occur with positive probability (Benaïm, 1999) for a class of Robbins Monro algorithms. Benaïm et al. (2005) generalised this approach for stochastic approximation algorithms whose average behavior is related to a differential inclusion instead. We pursue the analogy by extending to this setting the result of convergence with positive probability to an attractor.
Complete list of metadatas

Cited literature [21 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00383277
Contributor : Mathieu Faure <>
Submitted on : Tuesday, January 11, 2011 - 2:11:54 PM
Last modification on : Wednesday, November 28, 2018 - 2:48:22 PM
Long-term archiving on: : Tuesday, April 12, 2011 - 2:47:46 AM

Files

attractor_rev8.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Mathieu Faure, Gregory Roth. Stochastic approximations of set-valued dynamical systems: Convergence with positive probability to an attractor. Mathematics of Operations Research, INFORMS, 2010, 35 (3), pp.624-640. ⟨10.1287/moor.1100.0455⟩. ⟨hal-00383277v2⟩

Share

Metrics

Record views

193

Files downloads

372