Question

Relating convergence of characteristic function to almost sure convergence - Exercise 10.4.10 in Cohn's Book Measure Theory

score 273 · Answer 1 · 2021-01-05 18:14:13

273

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Relating convergence of characteristic function to almost sure convergence - Exercise 10.4.10 in Cohn's Book Measure Theory

Published on 05 Jan 2021 - 18:14

score 27 · Answer 2 · 2021-01-14 07:57:28

27

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Select the optimal parameter of characteristic functions to ensure the absolute value of the roots less than $1$.

Published on 14 Jan 2021 - 7:57

score 74 · Answer 3 · 2021-01-19 20:01:12

74

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Solving the probability difference equation $p_{n} = p(1 - p_{n-1}) + (1 - p)p_{n-1}$ yields a questionable closed-form equation?

Published on 19 Jan 2021 - 20:01

score 333 · Answer 4 · 2026-03-31 22:50:12

333

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Finding $\alpha$-stable distributions by (probably) Levy's continuity theorem

Published on 31 Mar 2026 - 22:50

score 109 · Answer 5 · 2021-01-24 16:53:56

109

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What's the time derivative of this characteristic function?

Published on 24 Jan 2021 - 16:53

score 129 · Answer 6 · 2026-02-24 03:26:28

129

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Proving two random vectors are following the same distribution using characteristic function?

Published on 24 Feb 2026 - 3:26

score 131 · Answer 7 · 2026-03-31 07:57:20

131

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Moment Generating Function of the Product of Two Independent Zero-Mean Normal Random Variables

Published on 31 Mar 2026 - 7:57

score 171 · Answer 8 · 2026-03-27 09:10:14

171

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Why is the characteristic function of the sign function $2i/t$?

Published on 27 Mar 2026 - 9:10

score 116 · Answer 9 · 2021-02-02 04:57:42

116

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Proof of the expected value of $|X|$ for a stable distribution?

Published on 02 Feb 2021 - 4:57

score 440 · Answer 10 · 2021-02-03 20:41:07

440

Views

Distribution of sum of product of normal random variables.

Published on 03 Feb 2021 - 20:41

score 81 · Answer 11 · 2021-02-06 12:08:47

81

Views

Calculate distribution of a random variable using characteristic function

Published on 06 Feb 2021 - 12:08

score 82 · Answer 12 · 2026-03-31 10:07:32

82

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Why is it better to use the characteristic function instead of the moment generating function when showing multivariate convergence?

Published on 31 Mar 2026 - 10:07

score 223 · Answer 13 · 2021-02-24 18:38:34

223

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Countable linear combinations of indicator functions has a canonical form and form a vector space

Published on 24 Feb 2021 - 18:38

score 75 · Answer 14 · 2021-03-02 21:40:47

75

Views

calculating characteristic function when variance is infinite

Published on 02 Mar 2021 - 21:40

score 240 · Answer 15 · 2021-03-03 01:26:04

240

Views

$\lim\limits_nx_n=0,\forall n \in \mathbb{N},\phi_X(x_n)=e^{-\sigma^2x^2_n} \implies \forall x \in \mathbb{R}, \phi_X(x)=e^{-x^2\sigma^2} $

Published on 03 Mar 2021 - 1:26

List Question

Relating convergence of characteristic function to almost sure convergence - Exercise 10.4.10 in Cohn's Book Measure Theory

Select the optimal parameter of characteristic functions to ensure the absolute value of the roots less than $1$.

Solving the probability difference equation $p_{n} = p(1 - p_{n-1}) + (1 - p)p_{n-1}$ yields a questionable closed-form equation?

Finding $\alpha$-stable distributions by (probably) Levy's continuity theorem

What's the time derivative of this characteristic function?

Proving two random vectors are following the same distribution using characteristic function?

Moment Generating Function of the Product of Two Independent Zero-Mean Normal Random Variables

Why is the characteristic function of the sign function $2i/t$?

Proof of the expected value of $|X|$ for a stable distribution?

Distribution of sum of product of normal random variables.

Calculate distribution of a random variable using characteristic function

Why is it better to use the characteristic function instead of the moment generating function when showing multivariate convergence?

Countable linear combinations of indicator functions has a canonical form and form a vector space

calculating characteristic function when variance is infinite

$\lim\limits_nx_n=0,\forall n \in \mathbb{N},\phi_X(x_n)=e^{-\sigma^2x^2_n} \implies \forall x \in \mathbb{R}, \phi_X(x)=e^{-x^2\sigma^2} $

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