3,136 reputation
1724
bio website math.wisc.edu/~janjigia
location Madison, WI
age
visits member for 2 years, 7 months
seen 56 mins ago

I am a graduate student in the probability group of the mathematics department at the University of Wisconsin - Madison.


Aug
20
reviewed Leave Open Convergence of infinite series of complex numbers
Aug
20
reviewed Close Maps that preserve Brownian motion law
Aug
19
reviewed Close why is (a proof of 1+1=2) necessary?
Aug
19
reviewed Close Integration of $e^{\cos x}\cos x$
Aug
19
reviewed Close When is Complex Normal Distribution equal to Normal distribution for real numbers
Aug
12
comment Show $\lim\limits_{n\to\infty}\mathbf E(f(X_n)g(Y))=\mathbf E(f(X)g(Y))$
I do not understand the second paragraph. Why is it clear that the limit as $R \to \infty$ of the supremum is zero? At some point, you need to use the fact that the hypotheses give you tightness, otherwise all you have from using compactly supported functions as your test functions is vague convergence.
Aug
10
comment How to talk about a random variable which only exists on an event
Have your new random variable be whatever you want on the nice set and be equal to the thing you are trying to bound off of it. That way it's defined everywhere and serves as a lower bound everywhere.
Aug
7
comment How to talk about a random variable which only exists on an event
The definition of a random variable is that it is a measurable function, so in particular it must be a function. That means you have to define it on the whole space.
Aug
2
comment The projective limit of probability spaces and the Kolmogorov-Daniell theorem
I think that the answer to your last question is that that is a peculiarity of the particular formulation of the extension theorem that you saw. Check the statement in Volume II of Bogachev's measure theory for example. The only thing you need for the proof to work is inner regularity (where the usual definition of compactness is replaced with the finite intersection property), which can be done in a purely measure theoretic framework.
Jul
31
comment Non-Probabilistic Argument for Divergence of the Simple Random Walk
You need an expectation and an absolute value in the statement, since $\frac{S_n}{\sqrt{n}}$ almost surely does not converge.
Jul
24
comment prove $\frac{e^{iuX_t}} {\mathrm{E}{[e^{iuX_t}]}}$ is martingale
Take a uniform random variable on the interval $[0,2\pi]$ or on the discrete set $\{0, \pi\}$ and set $u = 1$ for some simple examples. The exponential can have cancellations which sum to zero.
Jul
23
comment prove $\frac{e^{iuX_t}} {\mathrm{E}{[e^{iuX_t}]}}$ is martingale
Hint: for u sufficiently close to zero, the expectation in the denominator is bounded below and for all u, the expression in the numerator is bounded by $1$ in modulus. Notice also that it is possible that there exist u for which the expectation in the denominator is zero.
Jul
23
reviewed Close Find $dy/dx$ where $(7x+2y)^2=6x^4y^3$
Jul
18
reviewed Close Prove that if $X \sim N(\mu, \sigma^2)$, then $X \sim \mu + \sigma N(0, 1)$
Jul
16
comment Do differentiable functions preserve measure zero sets? Measurable sets?
Ah sorry about that, you are right.
Jul
6
reviewed Leave Open A year having more than one Friday the 13th?
Jul
5
revised First hitting time Geometric Brownian motion
edited body
Jul
5
comment First hitting time Geometric Brownian motion
Hint: Taking logs, it suffices to find the distribution of the hitting time of a Brownian motion with drift (or the time that BM hits a line) math.stackexchange.com/questions/133628/…
Jul
3
reviewed Close For a real valued function $f(x,y)$ on $\mathbb{R}^2$ which is in $L_2$, show that $f(x+ε,y+ε) → f(x,y)$ in $L_2$ when $ε → 0.$
Jul
3
reviewed Leave Open Extending holomorphic function to neighborhood of square