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3559Lower Barrier and Hit Probability From a Target Exit TimeBrownian motion starts at x = 1 with upper barrier 5. The lower barrier a is chosen so that the expected exit time is 8. What is the resulting probability of hitting 5 before a?随机过程中等derivation未尝试面试订阅3560Start Needed to Match Both a Probability and an Exit Time on [0, 10]Brownian motion starts at x inside [0, 10]. If the probability of hitting 10 before 0 is 0.6, what is the expected exit time?随机过程中等derivation未尝试面试订阅3561Why the Hitting Probability Is HarmonicWhy does the probability of hitting the upper barrier before the lower barrier end up being a linear function of the start x for Brownian motion?随机过程中等essay未尝试面试订阅3562Why Expected Exit Time Is Quadratic in the StartWhy does expected exit time from a bounded interval depend quadratically on the starting point rather than linearly?随机过程中等essay未尝试面试订阅3563Finite-Horizon Touching vs Eventual HittingWhy should finite-horizon barrier-touch probabilities not be confused with the interval-hitting probabilities used in bounded first-passage problems?随机过程中等essay未尝试面试订阅3564Why Optional Stopping Needs a Bounded Setup HereWhy are bounded intervals the natural place where optional-stopping arguments for Brownian hitting questions are most reliable?随机过程中等essay未尝试面试订阅