User Tom

3 votes

1 answer

115 views

Probability Theory by Klenke theorem 15.9. That a finite measure is characterized by its characteristic function. [closed]

asked Oct 31, 2022 at 20:13

3 votes

2 answers

81 views

Weak convergence is defined in terms of $C_{b}$ functions, but for $\mathbb{R}^{d}$ why is it sufficient to show convergence for $C_{c}$ functions? [duplicate]

asked Dec 14, 2022 at 0:45

2 votes

0 answers

57 views

Confused about the Tower Property of expectations

asked Sep 1 at 18:02

2 votes

1 answer

27 views

$X$ is $\sigma(Y_{1}, ..., Y_{n})$-measurable iff $X = H(Y_{1}, ..., Y_{n})$ for some $H$ measurable

asked Dec 1, 2022 at 21:03

1 vote

2 answers

53 views

LHS is convergent iff RHS is convergent. Why? Achim Klenke Probability theorem 6.7

asked Nov 12, 2022 at 2:35

1 vote

2 answers

46 views

If two random variables have the same distribution, how to show after subtracting a common r.v., they still have the same distribution?

asked Nov 2, 2022 at 3:09

1 vote

0 answers

25 views

Given bounds of n-th moments, how to bound the probability of a random variable's taking large values?

asked Nov 4, 2022 at 15:20

1 vote

0 answers

50 views

$X, Y$ iid, If $(\frac{X+Y}{\sqrt{2}}, \frac{X-Y}{\sqrt{2}})$ has the same distribution as $(X, Y)$, then $X$ is a normal r.v.

asked Nov 27, 2022 at 0:32

1 vote

1 answer

85 views

tower property applied to expectations conditioned on an event; definition of the latter

asked Sep 26 at 6:00

1 vote

0 answers

36 views

Are probability measures on $\mathbb{R}^{d}$ characterized by integrals of $C_{c}$ functions?

asked Dec 17, 2022 at 16:36

1 vote

1 answer

57 views

Is this form of Taylor's theorem correct? Güler's Foundations of Optimization theorem 1.3

asked Jan 12 at 16:27

1 vote

1 answer

34 views

Existence of partial derivatives implies existence of the derivative under this condition?

asked Jan 13 at 19:41

0 votes

1 answer

144 views

What does it mean to say something is twice Fréchet differentiable?

asked Jan 17 at 17:05

0 votes

1 answer

108 views

An equation about the 2nd order Fréchet derivative

asked Jan 17 at 19:10

0 votes

2 answers

88 views

Given convexity, $\lim_{\|x\| \xrightarrow{} \infty} f(x) = \infty$ is equivalent to $\liminf_{\|x\|\xrightarrow{} \infty} \frac{f(x)}{\|x\|} > 0$?

asked Apr 27 at 20:46

0 votes

0 answers

18 views

Prove this inequality about Markov Chains with Fatou's Lemma

asked Sep 18 at 20:31

0 votes

1 answer

45 views

About the maximum of $n$ uniform$([0, 1])$ r.v.'s

asked Nov 10, 2022 at 3:57

0 votes

0 answers

34 views

How to prove this almost surely convergence in $L^{\infty}$ norm?

asked Nov 11, 2022 at 16:09

0 votes

1 answer

24 views

Do measurable maps preserve uncorrelated random variables?

asked Nov 2, 2022 at 14:29

0 votes

1 answer

505 views

Multiply a random vector by an orthogonal matrix. The result has the same distribution.

asked Nov 22, 2022 at 3:56

0 votes

0 answers

61 views

What exactly is $dy$ in $\mu(dy)$ when we do integration in measure theory? Question about Markov kernel

asked Dec 3, 2022 at 23:36

0 votes

0 answers

48 views

How to prove this measure is $\sigma$-finite? Donald Cohn Measure Theory exercise 4.2.2

asked Dec 10, 2022 at 22:20

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22 Questions

Probability Theory by Klenke theorem 15.9. That a finite measure is characterized by its characteristic function. [closed]

Weak convergence is defined in terms of $C_{b}$ functions, but for $\mathbb{R}^{d}$ why is it sufficient to show convergence for $C_{c}$ functions? [duplicate]

Confused about the Tower Property of expectations

$X$ is $\sigma(Y_{1}, ..., Y_{n})$-measurable iff $X = H(Y_{1}, ..., Y_{n})$ for some $H$ measurable

LHS is convergent iff RHS is convergent. Why? Achim Klenke Probability theorem 6.7

If two random variables have the same distribution, how to show after subtracting a common r.v., they still have the same distribution?

Given bounds of n-th moments, how to bound the probability of a random variable's taking large values?

$X, Y$ iid, If $(\frac{X+Y}{\sqrt{2}}, \frac{X-Y}{\sqrt{2}})$ has the same distribution as $(X, Y)$, then $X$ is a normal r.v.

tower property applied to expectations conditioned on an event; definition of the latter

Are probability measures on $\mathbb{R}^{d}$ characterized by integrals of $C_{c}$ functions?

Is this form of Taylor's theorem correct? Güler's Foundations of Optimization theorem 1.3

Existence of partial derivatives implies existence of the derivative under this condition?

What does it mean to say something is twice Fréchet differentiable?

An equation about the 2nd order Fréchet derivative

Given convexity, $\lim_{\|x\| \xrightarrow{} \infty} f(x) = \infty$ is equivalent to $\liminf_{\|x\|\xrightarrow{} \infty} \frac{f(x)}{\|x\|} > 0$?

Prove this inequality about Markov Chains with Fatou's Lemma

About the maximum of $n$ uniform$([0, 1])$ r.v.'s

How to prove this almost surely convergence in $L^{\infty}$ norm?

Do measurable maps preserve uncorrelated random variables?

Multiply a random vector by an orthogonal matrix. The result has the same distribution.

What exactly is $dy$ in $\mu(dy)$ when we do integration in measure theory? Question about Markov kernel

How to prove this measure is $\sigma$-finite? Donald Cohn Measure Theory exercise 4.2.2