Dynamics of Morse-Smale urn processes

Publisher Website
Google Scholar
Abstract
We consider stochastic processes {xn}n≥0 of the form whereF: ℝm→ ℝmis C2, {λi}i≥1 is a sequence of positive numbers decreasing to 0 and {Ui}i≥1 is a sequence of uniformly bounded ℝm-valued random variables forming suitable martingale differences. We show that when the vector fieldFis Morse-Smale, almost surely every sample path approaches an asymptotically stable periodic orbit of the deterministic dynamical systemdy/dt=F(y). In the case of certain generalized urn processes we show that for each such orbit Γ, the probability of sample paths approaching Γ is positive. This gives the generic behavior of three-color urn models.

This publication has 17 references indexed in Scilit: