A note on the survival time of a dynamic system in an interval

The one-dimensional system dx(t=bu(t)dt+(ct/sup 2/)/sup 1/2/dW(t), where b ( not=0) and c (>or=0) are real constants and W(t) is a standard Brownian motion, is considered. The aim is to obtain the control u* that minimizes the expected value of a cost function with terminal cost equal to 0 or + infinity depending on whether the survival time in a given region is at least equal to or less than a fixed time.<
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