Optimal drift on
Trans. Amer. Math. Soc. 346 (1994), 159-175
Primary 60H10; Secondary 60J60, 60J65
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Abstract: Consider one-dimensional diffusions on the interval of the form , with 0 a reflecting boundary, , and . In this paper, we show that there is a unique drift which minimizes the expected time for to hit , starting from . In the deterministic case , the optimal drift is the function which is identically equal to . By contrast, if , then the optimal drift is the step function which is on the interval and is 0 otherwise. We also solve this problem for arbitrary starting point and find that the unique optimal drift depends on the starting point, , in a curious manner.
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