Abstract
The probability of visiting a goal set infinitely often is a typical criterion in the theory of gambling founded by Dubins and Savage (1965). This criterion is more difficult to handle than the usual criteria in dynamic programming (total return and average return per unit time). So the existence of optimal strategies was known only for a model with finite state space and finite action space. In the present paper that existence result will be extended to the case of a compact action space under the continuity assumptions known from the average return criterion. Also the methods of proof are borrowed from dynamie programming with the latter criterion.
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