Stochastic Approximation of Discontinuous Dynamics

Authors: 
Ziv Gorodeisky
Abstract: 

We consider stochastic dynamics whose expected (average) vector field is not necessarily continuous. We generalize the ordinary differential equation method for analyzing stochastic processes to this case, by introducing leading functions that “lead” the stochastic process across the discontinuities, which yields approximation results for the asymptotic behavior of the stochastic dynamic. We then apply the approximation results to the classical best-response dynamics used in game theory.

Date: 
December, 2008
Published in: 
Number: 
496