7 problems

Let $\mathbb{B}_n$ be the Bergman ball, let $p\in(0,\infty)$ and $\alpha>n$, and let $A^p_\alpha(\mathbb{B}_n)$ denote the weighted Bergman space of holomorphic functions with norm…

Let $\mu$ and $\nu$ be measures in convex order, and let the irreducible convex paving be the finest partitioning that constrains all martingale transports between them. A Borel se…

Let $\lambda_1$ and $\lambda_2$ be probability measures in convex order, let $\mathfrak{I}$ denote the interval supporting the relevant variables, and let $\mathcal{M}$ be the set…

Let $F_1,\dots,F_n$ be distributions with general margins supported on bounded intervals and having sufficient smoothness. Let $\mathcal D_n$ denote the set of possible distributio…

A posterior predictive p-value is a statistic of the form described by Rubin, in which the test does not depend on the parameter. The authors' conjecture. These p-values can be bou…

Herschkorn's conjecture. The inequality

Let $X$ be a semimartingale and let $\mathcal{P}$ be a partition of $[0,T]$. Write $RV(X,\mathcal{P})$ for the realized variance of $X$ along $\mathcal{P}$, and let $[X,X]_T$ denot…