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A general theory on first passage times with applications to adaptive decision making

Modern intelligent systems are expected to be able to learn from experience, making decisions on the basis of the available information and proceeding step by step to a desired goal. An important specification of such adaptive decision making method is the amount of time to accomplish a decision. In this paper, we propose a random walk model for such decision making method. The model involves random processes which have independent stationary increments. The decision times are formulated as first passage times dependent on the parameters of decision rules. Asymptotic and nonasymptotic results are developed for the analysis of first passage times.