Mathematics
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izimath
  • Member for 6 years, 11 months
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All Questions Answers
Score Newest
question
5
For any unitary matrix $U$, there exists a Hermitian matrix $H$ such that $U=e^{iH}$
Jul 12, 2015
question
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, 2018
question
4
$rank(M)=rank(M^2)$ whenever $M$ is skew-symmetric
Aug 28, 2019
question
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, 2019
question
3
$u(t,B_t)$ is a martingale if $u(t,x)$ is polynomial in each variables and satisfies the heat equation
Nov 12, 2019
question
3
Show for i.i.d. r.v., $Y_n /n \rightarrow 0$ a.s. $\Leftrightarrow$ $E|Y_1| < \infty$
Apr 24, 2018
question
3
Show $S^n \setminus \{p,q\} $ is diffeomorphic to $\mathbb R^n \setminus\{0\}$.
Jun 13, 2019
question
3
On the unit sphere $S^2$, show the antipodal map $A:S^2\to S^2$ is orientation reversing using definitions.
Apr 10, 2019
question
3
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, 2018
question
3
Show $(B_t )^2$ i.e. square of a Brownian motion is a Markov process. [duplicate]
Dec 12, 2018
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11
Finding distribution of $\int_0 ^T uW_u du$

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