9 problems

Gneiting's conjecture. Any characteristic function with an absolutely continuous component has the substitution property.

Let $X$ be a centred, non-degenerate random vector, and let $R(t)={\mathbb E}[\cos(t^\top X)]$ and $M(t)={\mathbb E}[\exp(t^\top X)]$ denote its real characteristic-function part a…

Genton–Loperfido's conjecture. The characteristic function of a generalized skew-elliptical distribution, or of a subclass of generalized skew-elliptical distributions, has the for…

Let $f$ be the characteristic function of a probability measure with a nontrivial absolutely continuous component, and let $\varphi$ be the density function of this component. Let…

Let $\bar{r}(\epsilon,p,n,\underline{\alpha})$ be the infimum of $r_n(\alpha)$ over $\alpha\in(\underline{\alpha},2]$, and let $\bar{r}$ and $\bar{u}$ denote the universal bounds i…

Let $S^{(0)}_{1}=\sum_{w\ne 1}S^{(0)}_{w1}$ be the total solvency shock transmitted to bank $1$ in step $0$, conditioned on the type $T_1=T$. Let $\hat f^{(0)}_\Delta(k'\mid T')$,…

Product decomposition conjecture. The characteristic function of any multiplicity-free cnu contractive associator in $B_n^*(\mathbb D)$ is the pointwise product of the characterist…

Let $f_j(x,v,\tau;\phi)$, for $j\in\{1,2\}$, denote the characteristic function solving the stated partial differential equation with initial condition…

Let $\{F_t\}_{t\geq 0}$ be a symmetric Feller process on $\mathbb{R}^d$ with symbol $q(x,\xi)$, and let $\Phi_t(x,\xi)$ denote its characteristic function. Assume that the symbol s…