List questions from probability-limit-theorems

Published on 10 Apr 2020 - 2:30

35

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A sequence of random variables with bounded first three moments

Published on 11 Apr 2020 - 19:49

40

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What integral theorem can justify this limit of probabilities, where we have a limit in the integrand and the limits of integration?

Published on 11 Apr 2020 - 22:47

42

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$\delta$-method on $\mathbb{R}^d$

Published on 25 Mar 2026 - 16:05

209

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Random equation

Published on 25 Mar 2026 - 22:02

1k

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Weak convergence of a sequence of gaussian random vector

Published on 14 Apr 2020 - 17:47

189

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Central Limit Theorem for Linear Combination of Poisson Variables

Published on 15 Apr 2020 - 16:38

50

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Convergence to $+\infty$ a.s along a subsequence

Published on 17 Apr 2020 - 17:14

80

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Rigorous definition of convergence in mean

Published on 19 Apr 2020 - 23:22

1000

Views

Detail on Portmanteau theorem

Published on 20 Apr 2020 - 17:26

340

Views

Using Lyapunov Condition show that a sequence of Poisson-Binomial random variables converge in distribution to the standard normal.

Published on 20 Apr 2020 - 19:39

71

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Please verify my proof for the lemma: "If $X_n \to_d X$ and $X_n + Y_n \to_d X$ with $X_n$ and $Y_n$ independent for each $n$, then $Y_n \to_p 0$"

Published on 21 Apr 2020 - 19:58

98

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Convergence in distribution and in probabiliity

Published on 21 Apr 2020 - 22:20

39

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Beginner limits in Calc

Published on 22 Apr 2020 - 0:55

201

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distribution convergence N(0,σ^2/n)

Published on 22 Apr 2020 - 1:37

List Question

Strong law of large numbers for triangular arrays

A sequence of random variables with bounded first three moments

What integral theorem can justify this limit of probabilities, where we have a limit in the integrand and the limits of integration?

$\delta$-method on $\mathbb{R}^d$

Random equation

Weak convergence of a sequence of gaussian random vector

Central Limit Theorem for Linear Combination of Poisson Variables

Convergence to $+\infty$ a.s along a subsequence

Rigorous definition of convergence in mean

Detail on Portmanteau theorem

Using Lyapunov Condition show that a sequence of Poisson-Binomial random variables converge in distribution to the standard normal.

Please verify my proof for the lemma: "If $X_n \to_d X$ and $X_n + Y_n \to_d X$ with $X_n$ and $Y_n$ independent for each $n$, then $Y_n \to_p 0$"

Convergence in distribution and in probabiliity

Beginner limits in Calc

distribution convergence N(0,σ^2/n)

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