Some results on convergence of stochastic approximations by differential inclusion methods

The ordinary differential equation (ODE) method is one of the most powerful tools for the convergence of stochastic approximations. The objective in this method is to associate to a given algorithm a deterministic differential equation with continuous right-hand side, through which the asymptotic behavior of the algorithm is investigated. In this paper a different method using differential inclusions is described: instead of a differential equation with continuous right-hand side, a differential inclusion is associated to the given algorithm. Several types of algorithms are considered for illustration