7 problems

Assume that the height function $H$ is associated with the Laplace exponent … where $\gamma\in(1,2]$ and $\kappa>0$. Let $\Phi_H$ be the limiting functional of the normalized Lévy…

Let $X$ be the canonical process under the excursion measure $\mathbf{N}$ of the strong Markov process $X-I$ at zero. Write $H$ for the height process, $\zeta$ for its lifetime, an…

Let $X$ be the canonical process under the excursion measure $\mathbf{N}$ of the strong Markov process $X-I$ at zero. Write $H$ for the height process, $\zeta$ for its lifetime, an…

Let $\mathfrak{T}\subset\mathbb{R}$ be an interval and let $\Psi=\{\psi_q:q\in\mathfrak{T}\}$ be an admissible family of branching mechanisms, where … with $b_q\in\mathbb{R}$ and…

Let $(\mathcal G_N)_{N\in\mathbb N}$ be a properly conditioned sequence of Galton–Watson trees, with scaling factors $a_N$, node measures $\mu_N^{\rm nod}$, skeleton pruning measur…

Let ${\mathcal G}_1$ be a rooted Galton–Watson tree, and consider pruning procedures on Galton–Watson trees in which cut points fall on edges or on nodes. The corresponding continu…

Jump-representation conjecture. The jump representation of the tree-valued Markov process holds without the Grey condition.