User BCLC

103 votes

2 answers

54k views

GRE Subject Test - Past Papers, Books, Advice

asked Sep 11, 2016 at 9:32

28 votes

10 answers

21k views

If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?

asked Apr 13, 2014 at 14:47

14 votes

5 answers

7k views

Using Fatou's Lemmas in proving Scheffe's Lemma Part (ii)

asked Oct 26, 2015 at 13:33

13 votes

4 answers

3k views

Why do we consider Borel sets instead of (Lebesgue) measurable sets?

asked Nov 3, 2015 at 12:08

13 votes

2 answers

2k views

Why do we need the absolute value signs when integrating the square of a function?

asked Aug 23, 2014 at 23:19

13 votes

3 answers

4k views

Variable leaving basis in linear programming - when does it happen?

asked Mar 7, 2016 at 20:22

12 votes

1 answer

8k views

Is a random variable constant iff it is trivial sigma-algebra-measurable?

asked May 14, 2015 at 17:14

11 votes

1 answer

2k views

Understanding probabilistic Borel-Cantelli Lemma "Corollary" in Royden and Fitzpatrick

asked Apr 4, 2014 at 5:12

10 votes

3 answers

13k views

Probability sum of 5 before sum of 7

asked Jun 16, 2016 at 9:14

9 votes

1 answer

1k views

Intuition for Conditional Expectation

asked Dec 7, 2016 at 15:43

8 votes

2 answers

10k views

Convert a piecewise linear non-convex function into a linear optimisation problem.

asked Apr 19, 2016 at 11:46

8 votes

1 answer

3k views

Show limsup/liminf is in tail field

asked May 13, 2015 at 18:49

8 votes

2 answers

606 views

Why is it that $\mathscr{F} \ne 2^{\Omega}$?

asked Oct 30, 2015 at 11:31

7 votes

1 answer

1k views

Given $\mathbb Q$ and $X_t$ is $\mathbb Q$-Brownian, find $\frac{d\mathbb Q}{d\mathbb P}$ / Uniqueness of Brownian or Radon-Nikodym derivative

asked Dec 17, 2015 at 1:08

7 votes

3 answers

481 views

Infinite dimensional vector space has almost complex structure if and only if it is 'even-dimensional'?

asked Jan 22, 2020 at 8:53

6 votes

2 answers

524 views

Leibniz' Rule: Prove $\int_0^y u_{tt}(x,t) dt = u_y (x,y) - u_y (x,0)$

asked Aug 27, 2018 at 2:10

6 votes

1 answer

495 views

what do holomorphic functions 'look like'? Please provide references.

asked Mar 15, 2021 at 10:01

6 votes

3 answers

560 views

Why all $\epsilon > 0$, in the $\varepsilon-\delta$ limit definition?

asked Feb 4, 2016 at 17:01

6 votes

5 answers

6k views

Why is the distance between two circles/spheres that don't intersect minimised at points that are in the line formed by their centers?

asked Aug 29, 2016 at 10:21

6 votes

2 answers

756 views

Is it correct to say that ($\color{red}{(} \limsup |W_k|/k\color{red}{)} \le 1) \supseteq \limsup \color{red}{(}|W_k|/k \le 1\color{red}{)}$?

asked Nov 10, 2015 at 11:54

5 votes

1 answer

459 views

Show the equivalence of these definitions of independence of random variables

asked Nov 3, 2015 at 15:02

5 votes

2 answers

200 views

Compute $\lim_{x \to 0} x \lfloor x - \frac{1}{x} \rfloor$

asked Sep 29, 2015 at 16:05

5 votes

2 answers

2k views

Are random variables independent of their tail sigma-algebra?

asked Jul 24, 2015 at 15:41

5 votes

1 answer

4k views

Questions on Kolmogorov Zero-One Law Proof in Williams

asked May 29, 2015 at 8:44

5 votes

1 answer

1k views

Prove that if expectations agree on a Pi-System, then they agree on the Sigma-Algebra generated by the Pi-System.

asked Sep 25, 2014 at 13:24

5 votes

1 answer

7k views

Prove optimal solution to dual is not unique if optimal solution to the primal is degenerate and unique.

asked Dec 3, 2014 at 11:52

5 votes

3 answers

13k views

Prove $A_t := W_t^3-3t W_t$ a martingale

asked Oct 7, 2014 at 18:18

5 votes

4 answers

1k views

Prove that $\lim_{n\to\infty} H_n/n = 0$ ($H_n$ is the $n$-th harmonic number) using certain techniques

asked Apr 4, 2014 at 9:31

5 votes

2 answers

958 views

Strong Law of Large Numbers - Converse

asked Jun 5, 2016 at 17:46

5 votes

1 answer

365 views

Show that $P(T \le n + N \mid \mathscr F_n) > \epsilon$ where T is a stopping time

asked Dec 19, 2015 at 19:35

Stack Exchange Network

548 Questions

GRE Subject Test - Past Papers, Books, Advice

If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?

Using Fatou's Lemmas in proving Scheffe's Lemma Part (ii)

Why do we consider Borel sets instead of (Lebesgue) measurable sets?

Why do we need the absolute value signs when integrating the square of a function?

Variable leaving basis in linear programming - when does it happen?

Is a random variable constant iff it is trivial sigma-algebra-measurable?

Understanding probabilistic Borel-Cantelli Lemma "Corollary" in Royden and Fitzpatrick

Probability sum of 5 before sum of 7

Intuition for Conditional Expectation

Convert a piecewise linear non-convex function into a linear optimisation problem.

Show limsup/liminf is in tail field

Why is it that $\mathscr{F} \ne 2^{\Omega}$?

Given $\mathbb Q$ and $X_t$ is $\mathbb Q$-Brownian, find $\frac{d\mathbb Q}{d\mathbb P}$ / Uniqueness of Brownian or Radon-Nikodym derivative

Infinite dimensional vector space has almost complex structure if and only if it is 'even-dimensional'?

Leibniz' Rule: Prove $\int_0^y u_{tt}(x,t) dt = u_y (x,y) - u_y (x,0)$

what do holomorphic functions 'look like'? Please provide references.

Why all $\epsilon > 0$, in the $\varepsilon-\delta$ limit definition?

Why is the distance between two circles/spheres that don't intersect minimised at points that are in the line formed by their centers?

Is it correct to say that ($\color{red}{(} \limsup |W_k|/k\color{red}{)} \le 1) \supseteq \limsup \color{red}{(}|W_k|/k \le 1\color{red}{)}$?

Show the equivalence of these definitions of independence of random variables

Compute $\lim_{x \to 0} x \lfloor x - \frac{1}{x} \rfloor$

Are random variables independent of their tail sigma-algebra?

Questions on Kolmogorov Zero-One Law Proof in Williams

Prove that if expectations agree on a Pi-System, then they agree on the Sigma-Algebra generated by the Pi-System.

Prove optimal solution to dual is not unique if optimal solution to the primal is degenerate and unique.

Prove $A_t := W_t^3-3t W_t$ a martingale

Prove that $\lim_{n\to\infty} H_n/n = 0$ ($H_n$ is the $n$-th harmonic number) using certain techniques

Strong Law of Large Numbers - Converse

Show that $P(T \le n + N \mid \mathscr F_n) > \epsilon$ where T is a stopping time