Fei Cao

Member for 4 years, 6 months
Last seen this week

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Amherst, Massachusetts, USA

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stochastic-processes

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Questions

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13

prove a challenging inequality or find a counterexample to it

Dec 30, 2020

7

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

Feb 28, 2021

7

A possible error in Villani's monograph “Hypocoercivity”

Mar 20, 2021

7

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

Aug 6, 2020

7

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

Oct 9, 2021

Answers

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4

Prove that $f(x) = \frac{5x^{2}}{1 + x^{2}}$ is bounded

Aug 20, 2020

4

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

Mar 5, 2021

4

Covariance of Brownian motion intuition

Mar 7, 2021

4

Show that $E_f(\log f) \ge E_f (\log g)$

Apr 10, 2021

4

$V[\sqrt{X}]\le\frac{V[X]}{E[X]}$ for non-negative $X$

Jan 6, 2022

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stochastic-processes

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probability-theory

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27

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stochastic-calculus

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11

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inequality

11

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18

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calculus

11

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12

posts

Reputation

+10

Infinitesimal generator of the Brownian motion on a sphere

+30

On the derivation of some asymptotic expressions involving combinatorics

+10

Expanding $\int_{\Omega}|D^2u|^2(x,t)\;\mathrm{d}x$

+10

Heat equation: Energy $\int_{\Omega}u(t, x) dx$ is decreasing with positive initial data and $u=0$ on the boundary

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