Question

How can I show that $\int_0^T f(s)dW_s\sim \mathcal N\left(0, \int_0^T f(s)^2ds\right)$?

score 357 · Answer 1 · 2026-03-26 17:33:35

357

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How can I show that $\int_0^T f(s)dW_s\sim \mathcal N\left(0, \int_0^T f(s)^2ds\right)$?

Published on 26 Mar 2026 - 17:33

score 129 · Answer 2 · 2026-03-27 02:01:20

129

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score 64 · Answer 3 · 2026-03-28 02:03:35

64

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Uncorrelatedness does not implie independence

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score 67 · Answer 4 · 2019-08-12 10:56:18

67

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score 721 · Answer 5 · 2019-08-13 12:51:59

721

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score 560 · Answer 6 · 2019-08-14 00:38:48

560

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score 81 · Answer 7 · 2026-04-01 12:50:04

81

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Evaluation of an expectation involving a product of normally distributed rvs

Published on 01 Apr 2026 - 12:50

score 49 · Answer 8 · 2019-08-16 16:25:59

49

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Probability answer verification for normal distribution

Published on 16 Aug 2019 - 16:25

score 66 · Answer 9 · 2026-04-01 12:51:57

66

Views

$E[\exp(XY)]$=? $X=Z+\epsilon_1$, $Y=Z+\epsilon_2$, $Z, \epsilon_1, \epsilon_2\sim N(0,1)$, i.i.d.

Published on 01 Apr 2026 - 12:51

score 708 · Answer 10 · 2026-03-27 01:44:10

708

Views

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score 62 · Answer 11 · 2019-08-18 14:25:39

62

Views

Showing the Strong law of large numbers for normal distributed random variables by integration.

Published on 18 Aug 2019 - 14:25

score 401 · Answer 12 · 2019-08-19 11:30:16

401

Views

Why do we say stock prices have lognormal distribution?

Published on 19 Aug 2019 - 11:30

score 1.5k · Answer 13 · 2026-03-26 03:13:35

1.5k

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Limiting distribution of $\frac1n \sum_{k=1}^{n}|S_{k-1}|(X_k^2 - 1)$ where $X_k$ are i.i.d standard normal

Published on 26 Mar 2026 - 3:13

score 538 · Answer 14 · 2019-08-21 19:19:54

538

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Distribution of $\frac{X_1-\bar{X}}{S}$ when $X_1,\ldots,X_n$ are i.i.d $N(\mu,\sigma^2)$

Published on 21 Aug 2019 - 19:19

score 24 · Answer 15 · 2026-03-27 18:25:57

24

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Diagonalizable matrix and normal distribution

Published on 27 Mar 2026 - 18:25

List Question

How can I show that $\int_0^T f(s)dW_s\sim \mathcal N\left(0, \int_0^T f(s)^2ds\right)$?

Density of Uniform distribution with respect to standard-normal distribution

Uncorrelatedness does not implie independence

Probability of getting a higher value from a normal distribution

How to calculate exact probability of an event from normal distribution?

How to find probabilities using normal distribution

Evaluation of an expectation involving a product of normally distributed rvs

Probability answer verification for normal distribution

$E[\exp(XY)]$=? $X=Z+\epsilon_1$, $Y=Z+\epsilon_2$, $Z, \epsilon_1, \epsilon_2\sim N(0,1)$, i.i.d.

Finding the True Mean: How to solve this?

Showing the Strong law of large numbers for normal distributed random variables by integration.

Why do we say stock prices have lognormal distribution?

Limiting distribution of $\frac1n \sum_{k=1}^{n}|S_{k-1}|(X_k^2 - 1)$ where $X_k$ are i.i.d standard normal

Distribution of $\frac{X_1-\bar{X}}{S}$ when $X_1,\ldots,X_n$ are i.i.d $N(\mu,\sigma^2)$

Diagonalizable matrix and normal distribution

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