JGWang's user avatar
JGWang's user avatar
JGWang's user avatar
JGWang
  • Member for 6 years, 11 months
  • Last seen this week
6 votes
Accepted

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

5 votes
Accepted

Independent random variables with infinite expectation and central limit theorem

5 votes

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

5 votes
Accepted

Potential Local Martingale property derived from its quadratic variation

5 votes
Accepted

Strongly orthogonal martingales

5 votes
Accepted

Continuity of gaussian stochastic process

4 votes
Accepted

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

4 votes
Accepted

Càdlàg process and a predictable stopping time

3 votes

Will weak convergence of continuous functions give a continuous function?

3 votes
Accepted

Differentiation inside a conditional expectation

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 $1- \frac{1}{n}$?

3 votes
Accepted

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

3 votes

Spectral measure of 1-dimensional Ornstein-Uhlenbeck process

3 votes

Continuity of poisson process

3 votes

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

3 votes
Accepted

Calculation problem with Central limit theorem

3 votes
Accepted

Is every càdlàg process locally bounded?

3 votes
Accepted

Weak convergence of sum implies convergence of summands

3 votes

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

3 votes
Accepted

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

3 votes
Accepted

Cumulative distribution of a martingale

3 votes
Accepted

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

3 votes

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

2 votes
Accepted

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

2 votes
Accepted

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

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.

2 votes

Concavity of a two variables function with zero Hessian

2 votes
Accepted

How to use integration by parts in an example

2 votes
Accepted

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

2 votes

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

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