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3630Covariation of 2W_t+3B_t with -W_t+2B_tLet X t = 2W t + 3B t and Y t = -W t + 2B t with independent W and B. What is [X,Y] 0.5 ?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3636Why Smooth Drift Terms Disappear from Quadratic VariationWhy do smooth finite-variation terms fail to contribute to quadratic variation even though they can dominate the path in level?随机过程中等essay未尝试面试订阅3637Why Independent Brownian Motions Have Zero CovariationWhy does independence of Brownian drivers force the covariation term to vanish?随机过程中等essay未尝试面试订阅3638Why Quadratic Variation Scales with the Square of a CoefficientWhy does multiplying a Brownian-driven process by c multiply its quadratic variation by c 2 rather than by c?随机过程中等essay未尝试面试订阅3639Why Quadratic Variation Identifies Diffusion StrengthWhy is quadratic variation often the cleanest object for reading off the local diffusion strength of a process?随机过程中等essay未尝试面试订阅3640Why a Time Change Alters Quadratic VariationWhy does replacing W t by W ct change quadratic variation even before any extra scaling coefficient is added?随机过程中等essay未尝试面试订阅3641Coefficient Making W_t^2-a t a MartingaleChoose a so that X t = W t 2 - a t is a martingale.随机过程中等derivation未尝试面试订阅3642Coefficient Making exp(aW_t-2t) a MartingaleChoose a so that X t = exp(aW t - 2t) is a martingale.随机过程中等derivation未尝试面试订阅3643Coefficient Making e^{a t} cos W_t a MartingaleChoose a so that X t = e a t cos W t is a martingale.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