15 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 $N$ be a Hawkes process with link functions $phi=(phi_k)_k$ and parameter $f_0=(nu_0,h_0)$ satisfying Assumption (ass-psi), and suppose the hierarchical squared exponential Gau…

Pareto-tail conjecture. At the cost of increasing the model's complexity, replacing the exponential jump law by a law with Pareto tails should yield even better results.

Let $\bbphi_{\text{d}}$ denote the multivariate Hawkes kernel and let $\mathbb{K}_{\text{d}}$ denote the multivariate quadratic kernel. Define … with, in general, $n\neq n_H+n_Q$.…

Let $Y$ denote the process arising in the linear-quadratic formulation, let $\widehat{X}$ be the wealth process, and let $\mathcal{A}$ be the admissible set of controls. Let…

Let $\Phi$ be the interaction function governing the interacting Hawkes processes, and let $\lambda^{A}$ and $\lambda^{B}$ denote the corresponding population intensities. Theorem…

Let $\Phi_{B\to A}$ be the interaction function from population $B$ to population $A$, and let … is the sufficient subcriticality condition described above. Convexity conjecture. T…

Let $T_{ps}$ denote the perfect-sampling algorithm's sample-path length, and let $T=40$ be a representative time by which the simulated Hawkes/GI/1 queue is close to stationarity o…

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…

Let $F$ be an absolutely continuous distribution function on $\operatorname{\mathbb{R}}$ with $F(0)=0$ and density $f$. Let $\tilde{F}$ be the symmetrized version of $F$, namely th…

Consider the point process with intensity … where $c_{0}>0$, $a_{0}$ is the decay parameter, $N$ is the point process, and $X(t)$ is a time-dependent covariate process. Stationarit…