9 problems

Uniform Lyapunov drift conjecture. One could strengthen the arguments to obtain uniform Lyapunov drift conditions over suitable “compact” parameter spaces, in order to use Theorem…

Classification conjecture. Every such process is, up to an invertible affine transformation, the process constructed in Example, allowing $\lambda$ to take values in $[0,\infty)$ r…

Strengthened rank bound conjecture. The non-centrality parameter should satisfy

Let $C$ be a symmetric cone, and let $B$ be an exotic drift, meaning an inward-pointing drift constructed in the paper that cannot be written as a sum of a Lie algebra element and…

Let $C\subseteq V$ be a symmetric cone. A linear map $B:V\to V$ is inward-pointing when … for all $u,v\in C$ satisfying $\langle u,v\rangle=0$. A Lie algebra element is a generator…

Let $R$ and $N$ be the time-homogeneous processes under $mathbb Q$, and for $(t,u,v)\in\mathcal Q$ define … Here $S_d$ denotes the space of real symmetric $d\times d$ matrices, and…

Let $R$ be the functional appearing in the affine transform equations on the cone $S_d^+$, and let $\mu$ be the jump measure. The parameters are $\alpha,\beta^{ij},\gamma,\mu$. Con…

Let $d\geq 2$, and consider the jump behavior of an affine process with state space $S_d^+$, where $S_d^+$ is the cone of positive semidefinite matrices. Finite-variation conjectur…

Let $S_d^+$ denote the cone of positive semidefinite $d\times d$ matrices. Let $B:S_d\to S_d$ be a linear map satisfying condition from the source, and let $H\in M_d$ and…