Risk sensitive control with ergodic cost criteria

Stochastic control problems on an infinite time horizon with exponential cost criteria are considered. The Donsker-Varadhan large deviation rate (1975, 1976) is used as a criterion to be optimized. The optimum rate is characterized as the value of an associated stochastic differential game, with an ergodic (expected average cost per unit time) cost criterion. By taking a small-noise limit a deterministic differential game with an average cost per unit time cost criterion is obtained. This differential game is related to robust control of nonlinear systems.<
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