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izimath

Apparently, this user prefers to keep an air of mystery about them.

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  • Member for 4 years, 4 months
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4 For any unitary matrix $U$, there exists a Hermitian matrix $H$ such that $U=e^{iH}$ Jul 12 '15
4 Show $\limsup _{t \to \infty} \frac{B_t}{\sqrt{t \ln t}} \leq 1 $ using the fact that $\frac{e^{B_t ^2 / (1+2t)}}{\sqrt{1+2t}}$ is a martingale. Nov 7
3 Show for i.i.d. r.v., $Y_n /n \rightarrow 0$ a.s. $\Leftrightarrow$ $E|Y_1| < \infty$ Apr 24 '18
3 Prove For $(X_n)_{n \geq1}$ independent RVs, $ X_n \rightarrow X \ \text{ a.s.} \Rightarrow \sum _{n\geq1} P(|X_n -X| \gt \varepsilon) \lt \infty$ Apr 25 '18
3 Construct a continuous function $g$ which vanishes on closed $F$ and “follows” a continuous function $f$ outside $F$. Mar 13
2 Show $\sup_x \sqrt{n}|F_n(x) -F(x)|=O_p(1)$ where $F_n$ is the empirical distribution function of a iid RVs with a density function. Jun 6 '18
2 Suppose $X_n \rightarrow X$ a.s. and for each $n$, $X_n \perp \textit F$. Then is it true that $X \perp \textit F$? Nov 23 '18
2 Show $ \int_ {-\infty} ^{\infty} (\arctan(x+a)) {{1}\over {\sqrt{2 \pi T}}} e^{-x^2 /2T} dx$ can assume any value in $(-\pi/2, \pi/2)$ Dec 1 '18
2 Let $X,Y$ be independent RVs. If there exists $c \in \mathbb R $ s.t. $P(X+Y=c)=1$, then $X,Y$ are constants Apr 26 '18
2 Finding conditional expectation $E[f|g]$ given $f(x):= x^2 /2$ and $g(x):=2(x-1/2)^2$ Apr 16 '18
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