Stochastic approximations and differential inclusions
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...
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Published in | SIAM journal on control and optimization Vol. 44; no. 1; pp. 328 - 348 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Philadelphia, PA
Society for Industrial and Applied Mathematics
01.01.2005
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 0363-0129 1095-7138 |
DOI: | 10.1137/s0363012904439301 |