10 problems

Bertoin–Yor conjecture. The absence of positive jumps in $\xi$ is necessary for $X_\xi$ to be moment-determinate.

Let $\xi=(\xi_s)_{s\geq 0}$ be the Lévy process in the factorisation … and let $\overline{F}_\Psi(x)=\mathbb{P}(I_\Psi>x)$ denote the tail of the exponential functional $I_\Psi$. R…

Let $I_\Psi$ be the exponential functional of a potentially killed Lévy process with Lévy measure tail $\overline{\Pi}(0)$ and Gaussian coefficient $\sigma^2$. Infinite differentia…

Let $\{\xi_t:t\geq 0\}$ be a Lévy process and let $I_t(\xi):=\int_0^t e^{-\xi_s}\,ds$. For $\delta>0$, define the sampled random walk $\xi^\delta:=\{\xi_n^\delta:n=0,1,\ldots\}$ by…

Positive-increase conditions conjecture. General conditions on the Lévy–Khintchine exponent $\Psi$ that yield positive increase for the Lévy measure $\mu_+$ of $\phi_+$ may be impo…

Let $\Psi$ be a Laplace exponent in the class considered in the paper, and let $f_\Psi$ denote the density associated with the exponential functional $I_\Psi$. Assume that either t…

Tail-equivalence conjecture. There exists a constant $c\in(0,\infty)$ such that

Uniqueness conjecture. If two density functions satisfy the potential equation $$, then they are equal almost everywhere.

Non-closure conjecture. $R_\xi$ will never be closed under convolution unless $\xi$ is deterministic.

Let $\xi=(\xi_s)_{s\geq 0}$ be a Lévy process and let … For some constant $c\in(0,\infty)$, tail-equivalence conjecture. … The conjecture is motivated by the heuristic that large v…