Saturday, August 12

MS55
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 {x_k} are closely related to trajectories of the mean vector field F(x) := (k+1) E (x_k+1 - x_k/ x_k = x) . Tools of deterministic dynamics, such as attractors and chain recurrence, yield information on the limit set of {x_k}, 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.

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