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izimath

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

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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 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
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 '19
3 $u(t,B_t)$ is a martingale if $u(t,x)$ is polynomial in each variables and satisfies the heat equation Nov 12 '19
3 Construct a continuous function $g$ which vanishes on closed $F$ and “follows” a continuous function $f$ outside $F$. Mar 13 '19
3 $rank(M)=rank(M^2)$ whenever $M$ is skew-symmetric Aug 28 '19
3 Show for i.i.d. r.v., $Y_n /n \rightarrow 0$ a.s. $\Leftrightarrow$ $E|Y_1| < \infty$ Apr 24 '18
3 Show $(B_t )^2$ i.e. square of a Brownian motion is a Markov process. [duplicate] Dec 12 '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
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