List questions from probability-limit-theorems

Published on 12 Jul 2023 - 8:01

32

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What can we say about the sum of independent random variables with finite expectation?

Published on 12 Jul 2023 - 16:02

164

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$X_n\to X$ and $Y_n\to Y$ in distribution. What we can say about the convergence of $X_n+Y_n$?

Published on 14 Jul 2023 - 20:29

94

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From almost surely to expectation

Published on 20 Jul 2023 - 13:37

109

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Can a sequence $X_n$ of positive random variables converge to infinity almost surely with expectations remaining bounded?

Published on 22 Jul 2023 - 0:37

26

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$X_n \to_p X$, how to get sign consistency at rate $a(n)$, i.e $a(n)P(sgn(X_n) \neq sgn(X)) \to 0$

Published on 23 Jul 2023 - 11:16

86

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What does Borel's large number theorem really mean?

Published on 26 Mar 2026 - 11:07

76

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Convergence of the absolute value of a random series

Published on 07 Aug 2023 - 17:41

23

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Local limit theorem for not-identically distributed series?

Published on 09 Aug 2023 - 18:20

29

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A question related to the convergence of characteristic functions

Published on 13 Aug 2023 - 5:57

134

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Does convergence in probability imply deterministic convergence for non-random sequences?

Published on 25 Mar 2026 - 11:12

41

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On the convergence of the infimum of an average

Published on 18 Aug 2023 - 18:53

42

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Convergence of random vectors to vector with independent marginals when marginal distribution function converges at points of continuity

Published on 23 Aug 2023 - 12:14

35

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Longest Common Subsequence (LCS) - Subadditive Ergodic Theorem - Limit Upper Bound

Published on 23 Aug 2023 - 13:42

16

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Generalized CLT for uncorrelated centered RVs?

Published on 24 Aug 2023 - 9:57

List Question

Central limit theorem for uncorrelated and identically distributed random variables

What can we say about the sum of independent random variables with finite expectation?

$X_n\to X$ and $Y_n\to Y$ in distribution. What we can say about the convergence of $X_n+Y_n$?

From almost surely to expectation

Can a sequence $X_n$ of positive random variables converge to infinity almost surely with expectations remaining bounded?

$X_n \to_p X$, how to get sign consistency at rate $a(n)$, i.e $a(n)P(sgn(X_n) \neq sgn(X)) \to 0$

What does Borel's large number theorem really mean?

Convergence of the absolute value of a random series

Local limit theorem for not-identically distributed series?

A question related to the convergence of characteristic functions

Does convergence in probability imply deterministic convergence for non-random sequences?

On the convergence of the infimum of an average

Convergence of random vectors to vector with independent marginals when marginal distribution function converges at points of continuity

Longest Common Subsequence (LCS) - Subadditive Ergodic Theorem - Limit Upper Bound

Generalized CLT for uncorrelated centered RVs?

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