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3603OU Long-Run Mean Implied by a Conditional Mean Target 3An OU process satisfies dX t = 0.6(theta - X t)dt + sigma dW t with X 0 = 10. If E[X 0.5] should equal 8.9, what theta is implied?随机过程中等derivation未尝试面试订阅3616Quadratic Variation of 2W_t Plus a Smooth DriftLet X t = 2W t + t 3 - sin t. What is [X] 2?随机过程中等derivation未尝试面试订阅3617Quadratic Variation of -3W_t Plus an Exponential TrendLet X t = -3W t + e t. What is [X] 1?随机过程中等derivation未尝试面试订阅3618Quadratic Variation of 0.5W_t Plus an Integrated DriftLet X t = 0.5W t + integral 0 t s ds. What is [X] 4?随机过程中等derivation未尝试面试订阅3619Quadratic Variation of Brownian Motion with Two Smooth CorrectionsLet X t = W t - t + cos t. What is [X] 3?随机过程中等derivation未尝试面试订阅3620Quadratic Variation of 1.2W_t Plus a Rational DriftLet X t = 1.2W t + t/(1+t). What is [X] 5?随机过程中等derivation未尝试面试订阅3631Coefficient Making [W_t+aB_t]_2 Equal 10Choose a so that [W t + aB t] 2 = 10 where W and B are independent Brownian motions.随机过程中等derivation未尝试面试订阅3632Coefficient Making [W_t+aB_t, 2W_t-B_t]_1 Equal ZeroChoose a so that [W t + aB t, 2W t - B t] 1 = 0 with independent W and B.随机过程中等derivation未尝试面试订阅3633Scale Making [cW_{4t}]_1 Equal 1Choose c so that [cW 4t ] 1 = 1.随机过程中等derivation未尝试面试订阅3634Coefficient Making [aW_t+B_t]_3 Equal 15Choose a so that [aW t + B t] 3 = 15 with independent W and B.随机过程中等derivation未尝试面试订阅3635Coefficient Making [aW_t-B_t, W_t+B_t]_2 Equal 6Choose a so that [aW t - B t, W t + B t] 2 = 6 with independent W and B.随机过程中等derivation未尝试面试订阅3645Classifying an Exponentially Weighted Stochastic IntegralClassify X t = integral 0 t e -s dW s as a martingale, submartingale, or supermartingale.随机过程中等essay未尝试面试订阅3646Classifying W_t^2+tClassify X t = W t 2 + t.随机过程中等essay未尝试面试订阅3647Classifying 3-W_t^2-tClassify X t = 3 - W t 2 - t.随机过程中等essay未尝试面试订阅3648Classifying exp(W_t)Classify X t = exp(W t).随机过程中等essay未尝试面试订阅3649Classifying -exp(W_t)Classify X t = -exp(W t).随机过程中等essay未尝试面试订阅3650Classifying max(W_t,0)Classify X t = max(W t,0).随机过程中等essay未尝试面试订阅3651Classifying -|W_t|Classify X t = -|W t|.随机过程中等essay未尝试面试订阅3652Classifying a Stopped Brownian MotionLet tau = inf t : |W t| = 1 . Classify X t = W t wedge tau .随机过程中等essay未尝试面试订阅3654Classifying exp(W_t-t/2)+tClassify X t = exp(W t - t/2) + t.随机过程中等essay未尝试面试订阅