All Questions

I am interested in the concentration of polynomials of random variables. I have been reading Boucheron, Lugosi, and Massart's "Concentration inequalities" and they give some references. ...

Suppose that $X\geq0$, and that the moment generating function of $X$ exists in an interval around 0. Given some $\delta>0$ and integer $k=1,2,...$, show that $$\inf_{k=0,1,...}\frac{E(|X|^k)}{\...