User JGWang

6 votes

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Can a martingale always be written as the integral with regard to Brownian motion?

answered Feb 15, 2022 at 8:06

5 votes

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Potential Local Martingale property derived from its quadratic variation

answered Jun 25, 2021 at 8:40

5 votes

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Strongly orthogonal martingales

answered Jun 19, 2017 at 8:42

5 votes

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Continuity of gaussian stochastic process

answered Jul 5, 2017 at 3:47

5 votes

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Independent random variables with infinite expectation and central limit theorem

answered Sep 13, 2022 at 9:03

4 votes

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Show that $\lim\limits_{T \rightarrow \infty} \frac{1}{2T} \int_{-T}^T |\varphi(t)|^2 dt = \sum_{x \in \mathbb{R}}(\mu (\{x\}))^2$

answered Jun 18, 2017 at 4:33

4 votes

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Càdlàg process and a predictable stopping time

answered Feb 23, 2017 at 8:00

4 votes

Convergence in $L^p$: Marcinkiewicz-Zygmund Strong Law of Large Numbers

answered Apr 1, 2020 at 7:30

3 votes

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Difference between Levy's modulus of continuity and Law of Iterated Logarithm

answered Feb 5, 2022 at 9:57

3 votes

Probability measure $P_X$ on the space of paths of a Lévy process $(X_t)_{t \ge 0}$ determined by $P_{X_1}$

answered Oct 27, 2021 at 12:08

3 votes

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Cumulative distribution of a martingale

answered Mar 19, 2022 at 3:50

3 votes

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Why is $\frac{1}{n} \sup_{k\le n} |T_k - k| \to_{a.s.} 0$ if $T_n/n \to E T_1 = 1$?

answered Mar 24, 2022 at 8:25

3 votes

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Is every càdlàg process locally bounded?

answered Apr 12, 2022 at 12:48

3 votes

Will weak convergence of continuous functions give a continuous function?

answered Mar 29, 2017 at 8:19

3 votes

Spectral measure of 1-dimensional Ornstein-Uhlenbeck process

answered Apr 8, 2017 at 8:15

3 votes

Continuity of poisson process

answered Apr 20, 2017 at 8:00

3 votes

Showing $X_n \to 0$ in distribution where $X_n = n^2$ with probability $\frac{1}{n}$ and $X_n = \frac{1}{n}$ with probability $1- \frac{1}{n}$?

answered Jan 5, 2017 at 2:52

3 votes

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$X_1$ and $X_2$ stochastically larger than $Y_1$ and $Y_2$ implies $X_1+X_2$ stochastically larger than $Y_1+Y_2$

answered Feb 13, 2017 at 2:36

3 votes

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Differentiation inside a conditional expectation

answered May 11, 2017 at 7:58

3 votes

Showing stochastic dominance given the expectation of two Poisson R.V.'s

answered Sep 23, 2017 at 9:52

3 votes

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Calculation problem with Central limit theorem

answered Jan 14, 2018 at 7:14

3 votes

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Weak convergence of sum implies convergence of summands

answered Sep 4, 2022 at 22:41

3 votes

If $(X_n,f(X_n))$ converges in distribution to $(X,Y)$, can we say that $Y=g(X)$ for some $g$?

answered Aug 3 at 7:57

2 votes

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Moment inequality and second order stochastic dominance

answered Sep 5, 2017 at 3:47

2 votes

Sum of two stopping times is a stopping time?

answered Oct 16, 2019 at 3:52

2 votes

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How to evaluate $\mathrm{Cov}(\vec x^T A \vec x,\vec x^T B \vec x )$ for $\vec x\sim N(\vec 0, \Sigma)$ and square matrices $A,B$?

answered Aug 30, 2017 at 2:20

2 votes

Almost sure convergence in the martingale convergence theorem

answered May 28, 2017 at 3:21

2 votes

Accepted

Dual predictable projection of a jump process

answered Jun 3, 2017 at 8:15

2 votes

$Y_n = \sum_{k=1}^n X_k 2^{-k}$ converges to $Y \in \ uniform(-1,1)$

answered Jun 20, 2017 at 2:52

2 votes

Accepted

$L^2$ limit has continuous cdf.

answered Feb 6, 2017 at 3:34

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171 Answers

Can a martingale always be written as the integral with regard to Brownian motion?

Potential Local Martingale property derived from its quadratic variation

Strongly orthogonal martingales

Continuity of gaussian stochastic process

Independent random variables with infinite expectation and central limit theorem

Show that $\lim\limits_{T \rightarrow \infty} \frac{1}{2T} \int_{-T}^T |\varphi(t)|^2 dt = \sum_{x \in \mathbb{R}}(\mu (\{x\}))^2$

Càdlàg process and a predictable stopping time

Convergence in $L^p$: Marcinkiewicz-Zygmund Strong Law of Large Numbers

Difference between Levy's modulus of continuity and Law of Iterated Logarithm

Probability measure $P_X$ on the space of paths of a Lévy process $(X_t)_{t \ge 0}$ determined by $P_{X_1}$

Cumulative distribution of a martingale

Why is $\frac{1}{n} \sup_{k\le n} |T_k - k| \to_{a.s.} 0$ if $T_n/n \to E T_1 = 1$?

Is every càdlàg process locally bounded?

Will weak convergence of continuous functions give a continuous function?

Spectral measure of 1-dimensional Ornstein-Uhlenbeck process

Continuity of poisson process

Showing $X_n \to 0$ in distribution where $X_n = n^2$ with probability $\frac{1}{n}$ and $X_n = \frac{1}{n}$ with probability $1- \frac{1}{n}$?

$X_1$ and $X_2$ stochastically larger than $Y_1$ and $Y_2$ implies $X_1+X_2$ stochastically larger than $Y_1+Y_2$

Differentiation inside a conditional expectation

Showing stochastic dominance given the expectation of two Poisson R.V.'s

Calculation problem with Central limit theorem

Weak convergence of sum implies convergence of summands

If $(X_n,f(X_n))$ converges in distribution to $(X,Y)$, can we say that $Y=g(X)$ for some $g$?

Moment inequality and second order stochastic dominance

Sum of two stopping times is a stopping time?

How to evaluate $\mathrm{Cov}(\vec x^T A \vec x,\vec x^T B \vec x )$ for $\vec x\sim N(\vec 0, \Sigma)$ and square matrices $A,B$?

Almost sure convergence in the martingale convergence theorem

Dual predictable projection of a jump process

$Y_n = \sum_{k=1}^n X_k 2^{-k}$ converges to $Y \in \ uniform(-1,1)$

$L^2$ limit has continuous cdf.