Duration problem on trajectories
Vladimir Viktorovich Mazalov, Mitsushi Tamaki · Stochastics · 2007
Imagine that an urn contains m minus balls and p plus balls. We draw balls from the urn one by one without replacement until we wish to stop. Determine , where is the value of the ball chosen at kth draw, . The problem which we consider in this paper is to stop with maximum duration of possessing the maximum value of the trajectory formed by . We derive the optimal stopping rule and then make some comparison of the asymptotics of the optimal rules between our problem and the related problems.