  In this article we consider the ergodic risk-sensitive control problem for a
large class of multidimensional controlled diffusions on the whole space. We
study the minimization and maximization problems under either a blanket
stability hypothesis, or a near-monotone assumption on the running cost. We
establish the convergence of the policy improvement algorithm for these models.
We also present a more general result concerning the region of attraction of
the equilibrium of the algorithm.
