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In this paper the stability theorem of Borkar and Meyn is extended to include the case when the mean field is a differential inclusion.
Analysis of recursive stochastic algorithms
L. Ljung · 1977
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Differential Inclusions: Set-Valued Maps and Viability Theory
J. Aubin and A. Cellina · 1984
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Set-Valued Analysis
J. Aubin and H. Frankowska · 1990
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A dynamical system approach to stochastic approximations
M. Benaïm · 1996
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Asymptotic pseudotrajectories and chain recurrent flows, with applications
M. Benaïm and M. W. Hirsch · 1996
Earlier work this paper cites.
Dynamics of stochastic approximation algorithms
M. Benaïm · 1999
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The O.D.E. method for convergence of stochastic approximation and reinforcement learning
S.P. Meyn V.S. Borkar · 1999
Cited alongside, same era.
Stochastic Approximation and Recursive Algorithms and Applications
H. Kushner and G.G. Yin · 2003
Cited alongside, same era.
Stability of stochastic approximation under verifiable conditions
C. Andrieu, E. Moulines, and P. Priouret · 2005
Cited alongside, same era.
Stochastic approximations and differential inclusions
M. Benaïm, S. Sorin, and J. Hofbauer · 2005
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Stochastic Approximation: A Dynamical Systems Viewpoint
V. S. Borkar · 2008
Later among the works it cites.
Perturbations of set-valued dynamical systems, with applications to game theory
M. Benaïm, S. Sorin, and J. Hofbauer · 2012
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Stochastic recursive algorithms for optimization: simultaneous perturbation methods
S. Bhatnagar, H.L. Prasad, and L.A. Prashanth · 2012
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