Some results on risk sensitive adaptive control of discrete time Markov processes

Adaptive control of discrete time Markov processes with infinite horizon risk sensitive cost functionals is considered. Continuity of the risk sensitive cost functional with respect to a parameter is studied. Two almost optimal adaptive procedures based on the large deviations of the cost functional and on discretized maximum likelihood estimation are introduced. To justify the adaptive procedure with observation of the cost some large deviations estimates of empirical distributions of finite sequences of successive states of Markov processes are obtained