Saturday, August 12

Stochastic Approximation and Differential Equations

4:00 PM-6:00 PM
Orchard & Pikake (Salon 7 & 8)

Stochastic approximation algorithms are discrete time stochastic processes arising in many applications. Sample paths {xk} are closely related to trajectories of the mean vector field F(x) := (k+1) E (xk+1 - xk/ xk = x) . Tools of deterministic dynamics, such as attractors and chain recurrence, yield information on the limit set of {xk}, sometimes proving almost sure convergence (or nonconvergence). Benaïm will introduce the subject; Hirsch and Schreiber will discuss Game Theory and Evolutionary Processes; Kushner will present estimates of convergence rates. This minisymposium should interest researchers in probability, differential equations, game theory and population dynamics.

Organizers: Michel Benaïm
Université de Cergy, France
Morris W. Hirsch
University of California, Berkeley, USA
4:00-4:25 Dynamics of Stochastic Approximation Algorithms
Michel Benaïm, Organizer
4:30-4:55 Smooth Fictitious Play in Infinitely Repeated Games
Morris W. Hirsch and Michel Benaïm, Organizers
5:00-5:25 Generalized Urn Models of Evolutionary Processes
Michel Benaïm, Organizer; Sebastian Schreiber, Western Washington University, USA; and Pierre Tarres, CMLA - Ecole Normale Supérieure de Cachan, France
5:30-5:55 Stochastic Approximation: Rate of Convergence for Constrained Problems
Harold J. Kushner and Robert Buche, Brown University, USA

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