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bio website math.wisc.edu/~janjigia
location Madison, WI
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visits member for 2 years, 6 months
seen 5 hours ago

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


2d
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.
2d
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
23
reviewed Close Two measures having the same moments
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
Jul
3
revised how to prove Exponential is strictly positive?
edited tags
Jul
3
revised How to prove Exponential is monotone?
edited tags
Jul
2
awarded  Curious
Jul
1
reviewed Close Subgroup of roots of unity of a field.
Jul
1
reviewed Close Solve logarithmic equation: $2\log_7 (x+2) - \log_7 (3x+10) = 0$
Jul
1
reviewed Close 2-norm of a canonical Jordan form and spectral radius
Jul
1
reviewed Close Prove that the norm of $E$ is generate by the inner product $\langle x,y \rangle =\frac{1}{4}\left(||x+y|^2-||x-y||^2\right)$
Jun
30
comment If $X_{i}$ are I.I.D and $n^{-1}\sum_{i=1}^{n}X_{i}$ converges a.s/in-distribution to a constant $a$ is it true that $a=\mathbb{E}[X_{i}] $?
I think iid Cauchy random variables are a counterexample to your second "it is well-known" bullet. Are you sure you don't mean to have a limsup there?
Jun
20
comment Brownian Motion first hitting time distribution
You may want to re-read the question and make sure it isn't asking for this en.wikipedia.org/wiki/Inverse-gamma_distribution