Problems in the control of continuous Markov processes on a semicompactum by two players with conflicting interests are studied. The basic content of the paper is a derivation of Bellman's equations in the case where control is exercised for an infinite time (Theorem 3), and in the case of a problem of optimal stopping (Theorem 6). The results are illustrated by two examples (Theorems 1 and 2).
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Н. В. Крылов (1971) studied this question.
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