Fei Cao's user avatar
Fei Cao's user avatar
Fei Cao's user avatar
Fei Cao
  • Member for 4 years, 4 months
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13 votes
1 answer
422 views

prove a challenging inequality or find a counterexample to it

7 votes
2 answers
307 views

Prove that $0\le\int_0^1\log(u){\rm d}x+\frac1{2\pi^2}\int_0^1\frac1{u^2}\left(\frac{{\rm d}u}{{\rm d}x}\right)^2{\rm d}x$

7 votes
0 answers
373 views

A possible error in Villani's monograph “Hypocoercivity”

7 votes
1 answer
404 views

Modified Energy Method for Transformed Fokker-Planck Equation (Tricky Integration by parts...)

7 votes
1 answer
399 views

A possible bug in a highly cited paper (Adam gradient descent)?

6 votes
5 answers
228 views

Show that $\frac{1}{n}\sum_{j=1}^\infty \left( 1 - (1-p_j)^n\right) \to 0$ as $n \to \infty$

6 votes
1 answer
181 views

Proper linearization of ODEs of the form $\dot{x}(t) + f(x(t)) + \sigma(t) = 0$?

6 votes
1 answer
214 views

Showing $\frac{f(a+2b)+f(a-2b)}{2f(a)}\leq\sqrt{1-\left(\frac{b}{a(1-a)}\right)^2}$ for $f(x)=\sqrt{x(1-x)}$ with some constraints

5 votes
3 answers
346 views

A tough definite integral using contour integration

5 votes
2 answers
254 views

Geometric implication of the Sobolev embedding

4 votes
1 answer
134 views

Bounding Euclidean norm by slanted 1-norm

4 votes
1 answer
104 views

Parseval-Plancherel type identity for probability generating function

4 votes
1 answer
206 views

Poincare inequality for Poisson random variables

4 votes
1 answer
200 views

Optimal Poincare constant (with constraints)

4 votes
1 answer
182 views

exact meaning of uniform integrability for empirical distributions

4 votes
0 answers
82 views

Understanding the fast sweeping algorithm for Eikonal equations

3 votes
0 answers
111 views

Meaning of $K'[\cdot]$ when $K$ is an symmetric Onsager (matrix) operator

3 votes
1 answer
134 views

Non-uniqueness of a Dirichlet's problem

3 votes
1 answer
86 views

A basic question on martingales and filtrations

3 votes
1 answer
92 views

A discrete Poincare inequality

3 votes
1 answer
27 views

Show that $K(t) = \int_0^t \mathrm{e}^{-Cs} \, D \, \mathrm{e}^{-C^\intercal s} \,\mathrm{d} s$ satisfies a given equation involving $K(\infty)$

3 votes
0 answers
78 views

Generalized second derivative of a concave and piecewise $C^2$ function

3 votes
1 answer
25 views

Lipschitz continuity of $\sqrt{f}$ for $f(x) = \sup_{\alpha \in T} \sum_{i=1}^d \left(\sum_{j=1}^D \alpha_j x_{ij}\right)^2$

3 votes
0 answers
99 views

Deriving inequalities from other inequalities

2 votes
1 answer
124 views

Show $\mathbb{E}\left[\left|\sum_{i=1}^n X_iY_i\right|\right] \leq 2\mathbb{E}\left[\left|\sum_{i=1}^n Y_i\right|\right]$

2 votes
1 answer
220 views

Random time change from Oksendal's SDE textbook

2 votes
1 answer
737 views

Wasserstein distance between two empirical measures

2 votes
0 answers
132 views

Show that $\int_{-\infty}^{a_1} (a_1-x)^r f(x) \mathrm{d} x$ and $\int_{a_n}^\infty (x - a_n)^r f(x) \mathrm{d} x$ are of order $\mathcal{O}(n^{-r})$

2 votes
1 answer
98 views

Show that $x^2 + 3\sin^2 x$ satisfies the Polyak–Łojasiewicz condition

2 votes
1 answer
75 views

Gronwall inequality for a $2$-dimensional system of linear differential inequalities