4 problems

Let $X\sim N(0,1)$), and let $Y=h(X)$, where $h\in\mathbb{K}[X]$ is a polynomial with $\deg(h)\geq 3$ and ${\rm I\kern-0.16em E}[h(X)]=0$. For $p_0\in\mathbb{K}_0[Y]$, let…

Stein-factor gap conjecture. For all $k>\lambda$,

Let $X$ and $Y$ be independent non-centered normal random variables, and let $W=XY$. A second-order Stein operator for $W$ is a differential operator acting on smooth functions wit…

Stein universality lemma. For every $h\in\mathcal{H}$, this equation admits a bounded solution $f_h$ that is $d$ times differentiable, with