Question

Characteristic function and point masses

score 282 · Answer 1 · 2026-03-24 18:06:03

282

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Characteristic function and point masses

Published on 24 Mar 2026 - 18:06

score 374 · Answer 2 · 2026-03-25 14:37:33

374

Views

Characteristic function of infinitely divisible measure has no zero.

Published on 25 Mar 2026 - 14:37

score 71 · Answer 3 · 2026-03-24 20:26:54

71

Views

If $\mathbb{E} e^{it(X+Y)} = \mathbb{E} e^{itX} \mathbb{E} e^{itY}$ then $X$ and $Y$ are uncorrelated

Published on 24 Mar 2026 - 20:26

score 135 · Answer 4 · 2026-03-25 16:02:26

135

Views

How to show Sub-independent Random Variables are uncorrelated.

Published on 25 Mar 2026 - 16:02

score 1.8k · Answer 5 · 2026-03-25 13:04:39

1.8k

Views

Characteristic function equal to $1$

Published on 25 Mar 2026 - 13:04

score 413 · Answer 6 · 2026-03-25 10:32:06

413

Views

Proof by characteristic functions that $X+Y$ and $2X$ are identically distributed

Published on 25 Mar 2026 - 10:32

score 63 · Answer 7 · 2026-03-25 04:19:46

63

Views

Prove that the given RV is normal

Published on 25 Mar 2026 - 4:19

score 68 · Answer 8 · 2026-03-24 16:55:04

68

Views

Prove that $\phi(t)= \frac{1}{2} + \frac{e^{t^2}}{4e^{t^2} - 2}$ defines characteristic function

Published on 24 Mar 2026 - 16:55

score 137 · Answer 9 · 2026-03-25 13:54:32

137

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Show that $\int_{\mathbb{R}} |\mathbb{E}(e^{i \xi X})|^2 \, d\xi < \infty$ implies $P(X=x)=0, \forall x\in\mathbb{R}$.

Published on 25 Mar 2026 - 13:54

score 431 · Answer 10 · 2026-03-25 02:30:57

431

Views

If $\phi$ is a characteristic function, then $1-|\phi(2t)|\leq 8\{1-|\phi(t)|\}$

Published on 25 Mar 2026 - 2:30

score 147 · Answer 11 · 2026-03-25 12:44:59

147

Views

Question involving Characteristic Functions and the Existence of a Distribution

Published on 25 Mar 2026 - 12:44

score 466 · Answer 12 · 2026-03-24 23:20:26

466

Views

Showing that the ratio of two standard independent normals is a Cauchy using Characteristic Functions

Published on 24 Mar 2026 - 23:20

score 71 · Answer 13 · 2026-03-25 04:23:52

71

Views

Showing that the Distribution of a Random Variable Must be Standard Normal using Characteristic Functions

Published on 25 Mar 2026 - 4:23

score 315 · Answer 14 · 2026-03-25 23:36:44

315

Views

Show that stochastic integral w.r.t. Brownian motion is normal distributed

Published on 25 Mar 2026 - 23:36

score 86 · Answer 15 · 2026-03-24 22:01:43

86

Views

A nice inequality about characteristic function

Published on 24 Mar 2026 - 22:01

List Question

Characteristic function and point masses

Characteristic function of infinitely divisible measure has no zero.

If $\mathbb{E} e^{it(X+Y)} = \mathbb{E} e^{itX} \mathbb{E} e^{itY}$ then $X$ and $Y$ are uncorrelated

How to show Sub-independent Random Variables are uncorrelated.

Characteristic function equal to $1$

Proof by characteristic functions that $X+Y$ and $2X$ are identically distributed

Prove that the given RV is normal

Prove that $\phi(t)= \frac{1}{2} + \frac{e^{t^2}}{4e^{t^2} - 2}$ defines characteristic function

Show that $\int_{\mathbb{R}} |\mathbb{E}(e^{i \xi X})|^2 \, d\xi < \infty$ implies $P(X=x)=0, \forall x\in\mathbb{R}$.

If $\phi$ is a characteristic function, then $1-|\phi(2t)|\leq 8\{1-|\phi(t)|\}$

Question involving Characteristic Functions and the Existence of a Distribution

Showing that the ratio of two standard independent normals is a Cauchy using Characteristic Functions

Showing that the Distribution of a Random Variable Must be Standard Normal using Characteristic Functions

Show that stochastic integral w.r.t. Brownian motion is normal distributed

A nice inequality about characteristic function

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