7 problems

For a sparse multivariate Hawkes process, let $A_T^{ij}$ denote the cross-area between coordinates $i$ and $j$ over a time horizon $T$, and let the associated excitation graph enco…

Boundary regularity conjecture. For every $x\in[0,A]$, there exists a version of $s\mapsto p^{![2]}_{r,i,c,k}(x,s,l,j)$ that is continuous at $0$ and at $A$. Moreover, there exist…

Let $a,b,c\in\mathbb{R}$ be parameters of the Markov chain $(X_n)$. Let $P$ be the polynomial associated with these parameters, and write $\operatorname{Disc}(P)$ for its discrimin…

Let $N$ denote the number of customers in a Hawkes/M/$\infty$ queue, with ${\mathscr J}(u)=e^{-\mu u}$ and $h(u)=e^{-u}$ for $u\geqslant 0$. Assume that the service-time distributi…

Let $F$ be a displacement distribution and let $N_0$ be the random counting measure constructed from the renewal and random-walk occupation measures in the paper, with distribution…

Let $F$ be an absolutely continuous displacement distribution, let $\lambda>0$, and let $B\in\mathcal{B}_b(\operatorname{\mathbb{R}})$. Let $N^{(g)}$ and $\lambda^{(g)}$ be defined…

Let $F$ be an absolutely continuous distribution function with $F(0)=0$ and density $f$, let $\tilde{F}$ be the symmetrized version of $F$, and let $\lambda>0$. A critical Hawkes p…