第 9 / 16 页
非代码面试题
显示 20 / 319 道匹配题目
答题状态：未尝试未正确已正确
ID题目领域难度题型进度权限
3673Symmetric Half-Width for Mean Exit Time 12Brownian motion starts at 2 inside [-L,L]. Using OST on W t 2-t, what L makes E[tau] = 12?随机过程中等derivation未尝试面试订阅3674Upper Barrier for Mean Exit Time 6 from x=1.5Brownian motion starts at 1.5 with lower barrier 0 and upper barrier b. Using OST on W t 2-t, what b makes E[tau] = 6?随机过程中等derivation未尝试面试订阅3675Average Exit Time with Uniform Start on [0,6]The starting point X is uniform on [0,6]. Brownian motion starts at X and stops on first exit from [0,6]. What is E[tau] on average?随机过程中等derivation未尝试面试订阅3676Drifted Brownian Upper-Hit Probability with Positive DriftA drifted Brownian motion satisfies dX t = 0.5dt + dW t, starts at 1, and stops on first exit from [0,4]. Using the exponential martingale, what is the probability it exits through 4?随机过程中等derivation未尝试面试订阅3677Drifted Brownian Upper-Hit Probability with Negative DriftA drifted Brownian motion satisfies dX t = -0.3dt + dW t, starts at 2, and stops on first exit from [0,5]. What is the probability it exits through 5?随机过程中等derivation未尝试面试订阅3678Start Needed for a 60% Drifted Upper-Hit ProbabilityA drifted Brownian motion satisfies dX t = 0.4dt + dW t and stops on first exit from [0,6]. For what start x does the upper-exit probability equal 0.6?随机过程中等derivation未尝试面试订阅3679Upper Barrier Needed for an 85% Drifted Hit ProbabilityA drifted Brownian motion satisfies dX t = 0.7dt + dW t, starts at 1, and stops on first exit from [0,b]. What upper barrier b makes the upper-exit probability equal 0.85?随机过程中等derivation未尝试面试订阅3680Drifted Brownian Upper-Hit Probability on a Short IntervalA drifted Brownian motion satisfies dX t = 0.2dt + dW t, starts at 2, and stops on first exit from [0,3]. What is the upper-exit probability?随机过程中等derivation未尝试面试订阅3681Upper-Hit Probability with Drift and Nonunit VolatilityA diffusion satisfies dX t = 0.4dt + 1.5dW t, starts at 1.5, and stops on first exit from [0,5]. What is the probability it exits through 5?随机过程中等derivation未尝试面试订阅3682Upper-Hit Probability with Negative Drift and Lower VolatilityA diffusion satisfies dX t = -0.2dt + 0.8dW t, starts at 1, and stops on first exit from [0,4]. What is the upper-exit probability?随机过程中等derivation未尝试面试订阅3683Start Needed for a Drifted Hit Probability with Nonunit VolatilityA diffusion satisfies dX t = 0.3dt + 1.2dW t and stops on first exit from [0,6]. For what start x does the upper-exit probability equal 0.65?随机过程中等derivation未尝试面试订阅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3691Density Tilt Making an Energy Factor Slow Down Under QUnder P, a factor satisfies dX t = 1.1 dt + 0.5 dW t. A new measure Q is defined by W t Q = W t + theta t. What theta makes the drift of X under Q equal 0.2?随机过程中等derivation未尝试面试订阅3692Density Tilt Turning a Positive Drift into a Mild Negative OneUnder P, a factor satisfies dX t = 0.4 dt + 0.8 dW t. A new measure Q is defined by W t Q = W t + theta t. What theta makes the drift of X under Q equal -0.08?随机过程中等derivation未尝试面试订阅