Question

Does $P(\liminf_{n \to \infty}\{|X_{n}|\leq \epsilon\})=1\iff \exists N \in \mathbb N, |X_{n}|\leq \epsilon, \forall n \geq N, P-$a.s.

score 190 · Answer 1 · 2019-02-13 15:04:01

190

Views

Does $P(\liminf_{n \to \infty}\{|X_{n}|\leq \epsilon\})=1\iff \exists N \in \mathbb N, |X_{n}|\leq \epsilon, \forall n \geq N, P-$a.s.

Published on 13 Feb 2019 - 15:04

score 158 · Answer 2 · 2019-02-13 18:16:42

158

Views

Modification of the law of large numbers for Binomial random variables.

Published on 13 Feb 2019 - 18:16

score 75 · Answer 3 · 2019-02-18 02:11:30

75

Views

Is this sequence almost sure convergent?

Published on 18 Feb 2019 - 2:11

score 150 · Answer 4 · 2019-02-27 13:15:19

150

Views

A random variable $X$ is $P$-a.s. constant iff $\sigma(X)$ is $P$-trivial - for which state spaces?

Published on 27 Feb 2019 - 13:15

score 77 · Answer 5 · 2019-04-01 22:18:34

77

Views

Problem with left limits.

Published on 01 Apr 2019 - 22:18

score 39 · Answer 6 · 2019-04-10 14:54:02

39

Views

Does the specific sequence of random variables converge almost surely to a given constant?

Published on 10 Apr 2019 - 14:54

score 117 · Answer 7 · 2019-04-16 16:46:43

117

Views

$X_n$ converges in probability but not almost surely

Published on 16 Apr 2019 - 16:46

score 512 · Answer 8 · 2019-04-21 14:16:49

512

Views

A criterion of convergence almost surely.

Published on 21 Apr 2019 - 14:16

score 172 · Answer 9 · 2019-04-21 22:49:53

172

Views

Convergence in probability of running maximum

Published on 21 Apr 2019 - 22:49

score 119 · Answer 10 · 2019-04-26 22:22:20

119

Views

$N(t)/t\to 1/\mu$

Published on 26 Apr 2019 - 22:22

score 52 · Answer 11 · 2019-05-12 11:45:22

52

Views

Showing that for $\{u_n,u\}_{n \geq 1} \subseteq L^p(\Omega)$ it is $u_n \to u$ in $L^p(\Omega)$.

Published on 12 May 2019 - 11:45

score 72 · Answer 12 · 2019-06-05 19:33:35

72

Views

Find a condition on the $a_{n}$ that guarantees the series $\sum_{i=0}^{^\infty} a_{n}X_{n}$ is almost surely convergent,

Published on 05 Jun 2019 - 19:33

score 92 · Answer 13 · 2019-06-14 03:07:05

92

Views

Properties of Functions in $W^{1,p}(\Omega)$ and Their Weak Derivatives

Published on 14 Jun 2019 - 3:07

score 57 · Answer 14 · 2019-06-24 11:33:16

57

Views

Are probability spaces generally assumed to be complete measure spaces?

Published on 24 Jun 2019 - 11:33

score 130 · Answer 15 · 2019-07-10 15:17:17

130

Views

Condition to have an almost everywhere property

Published on 10 Jul 2019 - 15:17

List Question

Does $P(\liminf_{n \to \infty}\{|X_{n}|\leq \epsilon\})=1\iff \exists N \in \mathbb N, |X_{n}|\leq \epsilon, \forall n \geq N, P-$a.s.

Modification of the law of large numbers for Binomial random variables.

Is this sequence almost sure convergent?

A random variable $X$ is $P$-a.s. constant iff $\sigma(X)$ is $P$-trivial - for which state spaces?

Problem with left limits.

Does the specific sequence of random variables converge almost surely to a given constant?

$X_n$ converges in probability but not almost surely

A criterion of convergence almost surely.

Convergence in probability of running maximum

$N(t)/t\to 1/\mu$

Showing that for $\{u_n,u\}_{n \geq 1} \subseteq L^p(\Omega)$ it is $u_n \to u$ in $L^p(\Omega)$.

Find a condition on the $a_{n}$ that guarantees the series $\sum_{i=0}^{^\infty} a_{n}X_{n}$ is almost surely convergent,

Properties of Functions in $W^{1,p}(\Omega)$ and Their Weak Derivatives

Are probability spaces generally assumed to be complete measure spaces?

Condition to have an almost everywhere property

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