题目3635 · 随机过程
Coefficient Making [aW_t-B_t, W_t+B_t]_2 Equal 6
Choose a so that [aW_t - B_t, W_t + B_t]_2 = 6 with independent W and B.
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中文题目题目3634 · 随机过程
Coefficient Making [aW_t+B_t]_3 Equal 15
Choose a so that [aW_t + B_t]_3 = 15 with independent W and B.
打开 →题目3632 · 随机过程
Coefficient Making [W_t+aB_t, 2W_t-B_t]_1 Equal Zero
Choose a so that [W_t + aB_t, 2W_t - B_t]_1 = 0 with independent W and B.
打开 →题目3631 · 随机过程
Coefficient Making [W_t+aB_t]_2 Equal 10
Choose a so that [W_t + aB_t]_2 = 10 where W and B are independent Brownian motions.
打开 →题目3628 · 随机过程
Covariation of 0.5W_t+B_t with 3W_t+2B_t
Let X_t = 0.5W_t + B_t and Y_t = 3W_t + 2B_t with independent W and B. What is [X,Y]_4?
打开 →题目3627 · 随机过程
Covariation of 2W_t-B_t with W_t+4B_t
Let X_t = 2W_t - B_t and Y_t = W_t + 4B_t with independent W and B. What is [X,Y]_2?
打开 →题目3630 · 随机过程
Covariation of 2W_t+3B_t with -W_t+2B_t
Let X_t = 2W_t + 3B_t and Y_t = -W_t + 2B_t with independent W and B. What is [X,Y]_{0.5}?
打开 →题目3629 · 随机过程
Covariation of W_t-B_t with W_t+B_t
Let X_t = W_t - B_t and Y_t = W_t + B_t with independent W and B. What is [X,Y]_3?
打开 →题目3626 · 随机过程
Covariation of W_t+2B_t with 3W_t-B_t
Let X_t = W_t + 2B_t and Y_t = 3W_t - B_t where W and B are independent Brownian motions. What is [X,Y]_1?
打开 →题目3617 · 随机过程
Quadratic Variation of -3W_t Plus an Exponential Trend
Let X_t = -3W_t + e^t. What is [X]_1?
打开 →题目3618 · 随机过程
Quadratic Variation of 0.5W_t Plus an Integrated Drift
Let X_t = 0.5W_t + integral_0^t s ds. What is [X]_4?
打开 →题目3620 · 随机过程
Quadratic Variation of 1.2W_t Plus a Rational Drift
Let X_t = 1.2W_t + t/(1+t). What is [X]_5?
打开 →题目3616 · 随机过程
Quadratic Variation of 2W_t Plus a Smooth Drift
Let X_t = 2W_t + t^3 - sin t. What is [X]_2?
打开 →题目3623 · 随机过程
Quadratic Variation of a Piecewise-Volatility Integral
Let X_t = integral_0^t sigma(s) dW_s where sigma(s)=1 on [0,1], sigma(s)=2 on (1,2], and sigma(s)=0 on (2,3]. What is [X]_3?
打开 →题目3625 · 随机过程
Quadratic Variation of a Rescaled Time Polynomial Loading
Let X_t = integral_0^t (s/3) dW_s. What is [X]_3?
打开 →题目3624 · 随机过程
Quadratic Variation of a Square-Root Loading
Let X_t = integral_0^t sqrt(1+s) dW_s. What is [X]_3?
打开 →题目3622 · 随机过程
Quadratic Variation of an Itô Integral with Descending Loading
Let X_t = integral_0^t (2-s) dW_s. What is [X]_1?
打开 →题目3621 · 随机过程
Quadratic Variation of an Itô Integral with Linear Loading
Let X_t = integral_0^t (1+s) dW_s. What is [X]_2?
打开 →题目3619 · 随机过程
Quadratic Variation of Brownian Motion with Two Smooth Corrections
Let X_t = W_t - t + cos t. What is [X]_3?
打开 →题目3633 · 随机过程
Scale Making [cW_{4t}]_1 Equal 1
Choose c so that [cW_{4t}]_1 = 1.
打开 →题目3640 · 随机过程
Why a Time Change Alters Quadratic Variation
Why does replacing W_t by W_{ct} change quadratic variation even before any extra scaling coefficient is added?
打开 →题目3637 · 随机过程
Why Independent Brownian Motions Have Zero Covariation
Why does independence of Brownian drivers force the covariation term to vanish?
打开 →题目3639 · 随机过程
Why Quadratic Variation Identifies Diffusion Strength
Why is quadratic variation often the cleanest object for reading off the local diffusion strength of a process?
打开 →题目3638 · 随机过程
Why Quadratic Variation Scales with the Square of a Coefficient
Why does multiplying a Brownian-driven process by c multiply its quadratic variation by c^2 rather than by c?
打开 →题目3636 · 随机过程
Why Smooth Drift Terms Disappear from Quadratic Variation
Why do smooth finite-variation terms fail to contribute to quadratic variation even though they can dominate the path in level?
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