Stochastic Approximations of Set-Valued Dynamical Systems: Convergence with Positive Probability to an Attractor
Published Online:4 Aug 2010https://doi.org/10.1287/moor.1100.0455
References
- Differential Inclusions: Set-Valued Maps and Viability Theory (1984) (Springer-Verlag, New York) Crossref, Google Scholar
- Integrals of set-valued functions. J. Math. Anal. Appl. (1965) 12(1):1–12Crossref, Google Scholar
- A dynamical system approach to stochastic approximations. SIAM J. Control Optim. (1996) 34:437Crossref, Google Scholar
- Dynamics of stochastic approximation algorithms. Séminaire de Probabilités Strasbourg (1999) 33:1–68Google Scholar
- Asymptotic pseudotrajectories and chain recurrent flows, with applications. J. Dynam. Differential Equations (1996) 8(1):141–176Crossref, Google Scholar
- A class of nonhomogeneous self interacting random processes with applications to learning in games and vertex-reinforced random walks. (2008) . http://arxiv4.library.cornell.edu/abs/0806.0806Google Scholar
- Stochastic approximations and differential inclusions. I. SIAM J. Optim. Control (2005) 44:328–348Crossref, Google Scholar
- Stochastic approximations and differential inclusions. II. Applications. Math. Oper. Res. (2006) 31(4):673–695Link, Google Scholar
- Stochastic Approximations and Adaptive Algorithms (1990) (Springer-Verlag, Berlin) Crossref, Google Scholar
- Omega limit sets of axiom A diffeomorphisms. J. Differential Equations (1975) 18:333–339Crossref, Google Scholar
- Isolated invariant sets and the Morse index. CBMS Regional Conference Series in Mathematics (1978) (American Mathematical Society, Providence, RI) . Number 38Google Scholar
- Algorithmes Stochastiques (1996) (Springer, Paris) Google Scholar
- Linear Operators. Part 1: General Theory (1958) (Interscience, New York) Google Scholar
- Learning mixed equilibria. Games Econom. Behav. (1993) 5(3):320–367Crossref, Google Scholar
- The Theory of Learning in Games (1998) (MIT Press, Cambridge, MA) Google Scholar
- Stochastic estimation of the maximum of a regression function. Ann. Math. Statist. (1952) 23(3):462–466Crossref, Google Scholar
- On the strategic stability of equilibria. Econometrica (1986) 54(5):1003–1037Crossref, Google Scholar
- Stochastic Approximation Methods for Constrained and Unconstrained Systems (1978) (Springer-Verlag, Berlin) Crossref, Google Scholar
- Stochastic Approximation and Recursive Algorithms and Applications (2003) (Springer, New York) Google Scholar
- Analysis of recursive stochastic algorithms. Automatic Control, IEEE Trans. On (1977) 22(4):551–575Crossref, Google Scholar
- A stochastic approximation method. Ann. Math. Statist. (1951) 22(3):400–407Crossref, Google Scholar
- Convex Analysis. Princeton Landmarks in Mathematics (1997) (Princeton University Press, Princeton, NJ) . [Reprint of the 1970 original, Princeton Paperbacks]Google Scholar

