The rate of convergence and the asymptotic distributions for some adaptive control problems

The rate of convergence is given for a strongly consistent, recursive estimator for the unknown average return rate of the risky asset in a bilinear stochastic differential equation for the wealth in a portfolio selection and consumption model. This rate is in a sample path sense. The asymptotic normality of the cost is shown for the adaptive control of a linear stochastic control system with quadratic cost where the parameters appear affinely in the drift term.