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February 1999 Stochastic approximation algorithms with constant step size whose average is cooperative
Michel Benaïm, Morris W. Hirsch
Ann. Appl. Probab. 9(1): 216-241 (February 1999). DOI: 10.1214/aoap/1029962603

Abstract

We consider stochastic approximation algorithms with constant step size whose average ordinary differential equation (ODE) is cooperative and irreducible. We show that, under mild conditions on the noise process, invariant measures and empirical occupations measures of the process weakly converge (as the time goes to infinity and the step size goes to zero) toward measures which are supported by stable equilibria of the ODE. These results are applied to analyzing the long-term behavior of a class of learning processes arising in game theory.

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Michel Benaïm. Morris W. Hirsch. "Stochastic approximation algorithms with constant step size whose average is cooperative." Ann. Appl. Probab. 9 (1) 216 - 241, February 1999. https://doi.org/10.1214/aoap/1029962603

Information

Published: February 1999
First available in Project Euclid: 21 August 2002

zbMATH: 0983.62046
MathSciNet: MR1682576
Digital Object Identifier: 10.1214/aoap/1029962603

Subjects:
Primary: 62L20
Secondary: 34C35, 34F05, 93E35

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.9 • No. 1 • February 1999
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