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Paresseux Nguyen's user avatar
Paresseux Nguyen's user avatar
Paresseux Nguyen's user avatar
Paresseux Nguyen
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Any answer on MSE is a distraction of me from my work.

My appreciated answers

  1. An entropy inequality

  2. A law of large numbers for bounded processes

  3. If $X$ is Gaussian, prove that $X-\lfloor X \rfloor \sim U(0,1)$ as its variance becomes large

  4. Show that $f(x)$ is a constant function if $\lim\limits_{h\to 0}\frac{1}{h^3}\int_{-h}^{h}f(x+t)\cdot t\,dt=0$ for all $x$

  5. About the inequality $x^{x^{x^{x^{x^x}}}} \ge \frac12 x^2 + \frac12$

  6. Prove that two random variates must be negatively correlated

  7. Why do the triangular numbers initially form long cycles mod $2^k$?

  8. Is $\sqrt{n}(\bar X_n - \bar X_m)$ tight?

  9. $\underset{x\to 1}{\text{lim}}\int_0^x \frac{\sqrt{t} f(t)}{\sqrt{f(x)-f(t)}} \, \mathrm dt=\frac{ \pi }{\sqrt{2}}$

  10. Given the sequence $a_1=1$,$a_{n+1}=1+\frac{n}{a_n}$, does the sequence $a_n+n-a_n^2$ converges?

  11. Measurability and convergence of sequence of functions

  12. Prove $\lim\limits_{n \to \infty} na_n=0.$

  13. Convergence in probability for each $P_k$ implies convergence in probability in $\sum_k \lambda_k P_k$

  14. Generalisation of Dominated Convergence Theorem

  15. Is this Stochastic Process bounded from above?

  16. Proof of Hopf Lax formula

  17. What is the asymptotic expansion of $x_n$ where $x_{n+1} = x_n+1/x_n$?

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Can I open a discussion thread on Math.SE?
Dec 16, 2020
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18
Show that $f(x)$ is a constant function if $\lim\limits_{h\to 0}\frac{1}{h^3}\int_{-h}^{h}f(x+t)\cdot t\,dt=0$ for all $x$
17
"Find $\lim_{n \to \infty}\frac{x_n}{\sqrt{n}}$ where $x_{n+1}=x_n+\frac{n}{x_1+x_2+\cdots+x_n}$" -where does this problem come from?
15
About the inequality $x^{x^{x^{x^{x^x}}}} \ge \frac12 x^2 + \frac12$
10
Prove that $\prod_{i=1}^n(1+x_i)\leq \sum_{i=0}^n\frac{S^i}{i!}$, where $x_i\in\mathbb{R^+}$.
9
Generalisation of Dominated Convergence Theorem