User Ricter

5 votes

1 answer

107 views

Triangular inequality and metrics

asked Oct 26, 2022 at 14:56

5 votes

1 answer

98 views

Show that $E(X) = \sum^{\infty}_{n=0} P(X > n)$

asked Jan 23 at 18:38

5 votes

1 answer

147 views

Show that $\lim\limits_{n\to\infty}D_n$ exists if and only if $\lim\limits_{n\to\infty}E_n=\emptyset$

asked Jan 30 at 18:43

4 votes

1 answer

98 views

Martingale convergence theorem and martingale property

asked Jan 7 at 8:26

4 votes

4 answers

105 views

Stopping time max $\{n: \ X_1 + \cdots + X_n \le t \}$

asked Jan 7 at 8:56

3 votes

1 answer

81 views

Suppose $|X_n|\leqslant Y$ a.s. for all $n\in\Bbb N$. Show that $\sup|X_n|\leqslant Y$ a.s. too

asked Jan 2 at 16:32

2 votes

1 answer

120 views

L2-Bounded Martingales

asked Jan 1 at 8:39

2 votes

2 answers

111 views

equality between symmetric differences

asked Oct 27, 2022 at 7:50

2 votes

1 answer

127 views

Limsup of a sequence smaller than $x$

asked Oct 10, 2022 at 17:01

2 votes

1 answer

66 views

Variance and mean of a bernoulli [closed]

asked Jan 13 at 9:23

2 votes

2 answers

187 views

Limsup and liminf of a set

asked Oct 25, 2022 at 7:17

1 vote

1 answer

64 views

Compute Cov$(A, A \wedge B)$

asked Jan 3 at 17:04

1 vote

0 answers

41 views

Showing that the stopped filtration $\mathcal{F}_{s \vee t} = \mathcal{F}_s \cup \mathcal{F}_t$

asked Jan 8 at 13:45

1 vote

2 answers

105 views

Prove that if $X_n \to X$ in probability, then $X_n \to X$ in $L^1$.

asked Jan 9 at 19:53

1 vote

1 answer

72 views

Show that limsup $\frac{X_r}{r} = \infty $ almost surely

asked Jan 9 at 20:12

1 vote

1 answer

57 views

Show that $E[X] \leqslant m-1+nP[X \geq m]$

asked Jan 12 at 16:44

1 vote

1 answer

127 views

Characteristic function of a poisson random variable [duplicate]

asked Jan 12 at 20:13

1 vote

1 answer

86 views

Markov property and memoryless property

asked Jan 1 at 11:31

1 vote

1 answer

70 views

Uniqueness of the limit in measure on a NON-sigma-finite space

asked Dec 28, 2022 at 21:14

1 vote

1 answer

193 views

Borel Cantelli and convergence almost surely

asked Dec 31, 2022 at 9:48

0 votes

0 answers

29 views

Uniqueness of the limit and finiteness of the measure space

asked Dec 31, 2022 at 16:56

0 votes

1 answer

53 views

If A is a σ-algebra, then A = σ(A).

asked Sep 25, 2022 at 10:37

0 votes

0 answers

48 views

set measurable iff characteristic function is measurable [duplicate]

asked Oct 7, 2022 at 8:39

0 votes

1 answer

41 views

Characteristic function of a gaussian vector $R^4$

asked Jan 3 at 15:27

0 votes

1 answer

34 views

Measure inequalities and sets

asked Oct 13, 2022 at 12:13

0 votes

1 answer

55 views

Limit of singletons

asked Oct 13, 2022 at 21:12

0 votes

0 answers

27 views

Sequence of random variables and liminf

asked Oct 15, 2022 at 15:30

0 votes

0 answers

79 views

show that this satisfy the triangular inequality

asked Oct 27, 2022 at 19:25

0 votes

1 answer

51 views

Pointwise convergence and liminf

asked Dec 28, 2022 at 21:05

0 votes

1 answer

65 views

Showing that the stopped filtration $\mathcal{F}_{s \wedge t} = \mathcal{F}_s \cap \mathcal{F}_t$

asked Jan 8 at 9:38

Stack Exchange Network

38 Questions

Triangular inequality and metrics

Show that $E(X) = \sum^{\infty}_{n=0} P(X > n)$

Show that $\lim\limits_{n\to\infty}D_n$ exists if and only if $\lim\limits_{n\to\infty}E_n=\emptyset$

Martingale convergence theorem and martingale property

Stopping time max $\{n: \ X_1 + \cdots + X_n \le t \}$

Suppose $|X_n|\leqslant Y$ a.s. for all $n\in\Bbb N$. Show that $\sup|X_n|\leqslant Y$ a.s. too

L2-Bounded Martingales

equality between symmetric differences

Limsup of a sequence smaller than $x$

Variance and mean of a bernoulli [closed]

Limsup and liminf of a set

Compute Cov$(A, A \wedge B)$

Showing that the stopped filtration $\mathcal{F}_{s \vee t} = \mathcal{F}_s \cup \mathcal{F}_t$

Prove that if $X_n \to X$ in probability, then $X_n \to X$ in $L^1$.

Show that limsup $\frac{X_r}{r} = \infty $ almost surely

Show that $E[X] \leqslant m-1+nP[X \geq m]$

Characteristic function of a poisson random variable [duplicate]

Markov property and memoryless property

Uniqueness of the limit in measure on a NON-sigma-finite space

Borel Cantelli and convergence almost surely

Uniqueness of the limit and finiteness of the measure space

If A is a σ-algebra, then A = σ(A).

set measurable iff characteristic function is measurable [duplicate]

Characteristic function of a gaussian vector $R^4$

Measure inequalities and sets

Limit of singletons

Sequence of random variables and liminf

show that this satisfy the triangular inequality

Pointwise convergence and liminf

Showing that the stopped filtration $\mathcal{F}_{s \wedge t} = \mathcal{F}_s \cap \mathcal{F}_t$