List questions from probability-limit-theorems

Published on 14 Oct 2021 - 15:13

127

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Exponential function limit with error term

Published on 20 Oct 2021 - 9:25

83

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Almost sure convergence of the maximum of iid exponential radom variables

Published on 21 Oct 2021 - 4:24

44

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Conditions for $\mathbb{E}|g(X_n)-g(X)|\to 0,g\in C_b(\mathbb{R})$ when $X_n\overset{d}{\to}X$

Published on 22 Oct 2021 - 10:10

172

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Limit question: Does $(k-n)/\sqrt{n} \to x$ imply $k-n \to x\sqrt{n}?$

Published on 25 Oct 2021 - 5:30

591

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convergence in distribution and uniform integrability

Published on 25 Oct 2021 - 12:16

156

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Law of Large Numbers and Convergence in Probability of Quadratic Form

Published on 31 Mar 2026 - 10:15

33

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Calculate limit in probability sense, show it by definition $X_n \rightarrow_P X$

Published on 28 Oct 2021 - 10:51

180

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How to prove $X_n =e^{aS_n-bn} \to 0$ a.s.(where $S_n$ is the sum of standard normal random variables)?

Published on 02 Nov 2021 - 11:02

71

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Clarifying $L^p$ convergence

Published on 03 Nov 2021 - 0:46

241

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Problem from Sidney Resnick A Probability Path.

Published on 04 Nov 2021 - 11:09

124

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Convergence in distribution and sequence converging to $0$

Published on 04 Nov 2021 - 17:03

86

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$Y_n \overset{p}{\rightarrow} Y$ if $X_n \overset{p}{\rightarrow} X$ and $Y_n\overset{d}{=}X_n$ and $Y\overset{d}{=}X$?

Published on 08 Nov 2021 - 0:02

85

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Does Skorohod Dudley Wichura theorem imply Continuous Mapping Theorem?

Published on 23 Feb 2026 - 21:35

157

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Showing that $ \operatorname {Var} ( X ) \le 1 $ when $ | X | \le 1 $ a.s., and that the maximum is attained

Published on 08 Nov 2021 - 16:26

List Question

Nested convergence of random variables: a.s. and in distribution

Exponential function limit with error term

Almost sure convergence of the maximum of iid exponential radom variables

Conditions for $\mathbb{E}|g(X_n)-g(X)|\to 0,g\in C_b(\mathbb{R})$ when $X_n\overset{d}{\to}X$

Limit question: Does $(k-n)/\sqrt{n} \to x$ imply $k-n \to x\sqrt{n}?$

convergence in distribution and uniform integrability

Law of Large Numbers and Convergence in Probability of Quadratic Form

Calculate limit in probability sense, show it by definition $X_n \rightarrow_P X$

How to prove $X_n =e^{aS_n-bn} \to 0$ a.s.(where $S_n$ is the sum of standard normal random variables)?

Clarifying $L^p$ convergence

Problem from Sidney Resnick A Probability Path.

Convergence in distribution and sequence converging to $0$

$Y_n \overset{p}{\rightarrow} Y$ if $X_n \overset{p}{\rightarrow} X$ and $Y_n\overset{d}{=}X_n$ and $Y\overset{d}{=}X$?

Does Skorohod Dudley Wichura theorem imply Continuous Mapping Theorem?

Showing that $ \operatorname {Var} ( X ) \le 1 $ when $ | X | \le 1 $ a.s., and that the maximum is attained

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