The equivalence between infinite-horizon optimal control of stochastic systems with exponential-of-integral performance index and stochastic differential games

A new method, based on the theory of large deviations from the invariant measure, is introduced for the analysis of stochastic systems with an infinite-horizon exponential-of-integral performance index. It is shown that the infinite-horizon optimal exponential-of-integral stochastic control problem is equivalent to a stationary stochastic differential game for an auxiliary system. As an application of the developed technique, the infinite-horizon risk-sensitive LQG problem is analyzed for both the completely observed and partially observed case.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>