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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Independent random variables with infinite expectation and central limit theorem

answered Sep 13, 2022 at 9:03

5 votes

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

answered Apr 1, 2020 at 7:30

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

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

3 votes

Will weak convergence of continuous functions give a continuous function?

answered Mar 29, 2017 at 8:19

3 votes

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Differentiation inside a conditional expectation

answered May 11, 2017 at 7:58

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

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 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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Is every càdlàg process locally bounded?

answered Apr 12, 2022 at 12:48

3 votes

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Weak convergence of sum implies convergence of summands

answered Sep 4, 2022 at 22:41

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

answered Feb 5, 2022 at 9:57

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

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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Square-integrable martingale that converges almost surely but not in $L^2$

answered Jul 1 at 3:28

2 votes

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Does weak convergence to a continuous distribution imply strong convergence of measures?

answered Jul 5 at 7:50

2 votes

Accepted

Show that for any $a > 1/2$, $Y_n = s_n^{-2}(\log{s_n^2})^{-a} \sum_{k = 1}^n X_k$ converges to zero almost surely.

answered Feb 8 at 2:18

2 votes

Concavity of a two variables function with zero Hessian

answered Sep 19 at 9:01

2 votes

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How to use integration by parts in an example

answered Dec 23, 2021 at 2:20

2 votes

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Approximating the spectral density of white noise by a moving average process

answered Jun 11, 2021 at 9:54

2 votes

Definition of optional sigma algebra require the left hand limit or just right continuous adapted processes?

answered Jan 20, 2022 at 3:06

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174 Answers

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

Independent random variables with infinite expectation and central limit theorem

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

Potential Local Martingale property derived from its quadratic variation

Strongly orthogonal martingales

Continuity of gaussian stochastic process

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

Will weak convergence of continuous functions give a continuous function?

Differentiation inside a conditional expectation

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 $Y_1+Y_2$

Spectral measure of 1-dimensional Ornstein-Uhlenbeck process

Continuity of poisson process

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

Calculation problem with Central limit theorem

Is every càdlàg process locally bounded?

Weak convergence of sum implies convergence of summands

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

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

Cumulative distribution of a martingale

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

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

Square-integrable martingale that converges almost surely but not in $L^2$

Does weak convergence to a continuous distribution imply strong convergence of measures?

Show that for any $a > 1/2$, $Y_n = s_n^{-2}(\log{s_n^2})^{-a} \sum_{k = 1}^n X_k$ converges to zero almost surely.

Concavity of a two variables function with zero Hessian

How to use integration by parts in an example

Approximating the spectral density of white noise by a moving average process

Definition of optional sigma algebra require the left hand limit or just right continuous adapted processes?