Goal and Average Cost Problems in Decision Processes with Finite State Spaces.
GEORGIA INST OF TECH ATLANTA SCHOOL OF MATHEMATICS
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The principal investigator carried out research in probability theory, and, in particular, in the theory of decision processes. First, it was shown that in every finite state decision process gambling problem with single fixed goal, there always exists a stationary strategy which not only nearly maximizes the probability of reaching the goal, but nearly minimizes the expected time to the goal. This result was considerably generalized to include decision processes with arbitrary state spaces and total cost criteria. Investigations of these processes led to results in optimal stopping theory, and in classical probability theory. Universal, best possible constants were found which compared the optimal expected return of a decision maker with the expected supremum of a sequence of independent random variables. A generalization of the classical Borel-Cantelli Lemma was found, as was a very general conditioning principle for strong laws of several forms. The question of existence of good Markov strategies in finite state decision processes with average reward criteria was addressed, and various partial results were obtained, although the general case was not settled. Author
- Statistics and Probability