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3684Barrier Needed for a 90% Drifted Hit Probability with Sigma OneA diffusion satisfies dX t = 0.5dt + 1dW t, starts at 2, and stops on first exit from [0,b]. What upper barrier b makes the upper-exit probability equal 0.9?随机过程中等derivation未尝试面试订阅3685Short-Interval Hit Probability with Small Drift and Small VolatilityA diffusion satisfies dX t = 0.1dt + 0.6dW t, starts at 1.2, and stops on first exit from [0,3]. What is the probability of hitting the upper barrier first?随机过程中等derivation未尝试面试订阅3686Why Bounded Stopping Times Make OST SaferWhy are bounded stopping times the cleanest setting for applying optional stopping in interview problems?随机过程中等essay未尝试面试订阅3687Why Drifted Brownian Motion Needs an Exponential MartingaleWhy is the exponential martingale the natural OST tool once Brownian motion has nonzero drift?随机过程中等essay未尝试面试订阅3688Why Expected Exit Time Comes from W_t^2-tWhy does the compensated square W t 2-t become the natural OST object for expected exit times?随机过程中等essay未尝试面试订阅3689Why OST Can Fail for Unbounded Stopping RulesWhy is it dangerous to apply optional stopping mechanically when the stopping rule is unbounded?随机过程中等essay未尝试面试订阅3690Why OST and Reflection Solve Different Brownian QuestionsWhy should OST problems not be confused with reflection-principle problems even though both often involve Brownian barriers?随机过程中等essay未尝试面试订阅