2 problems

Let a whole-plane LLE be driven by a Lévy process without drift, and suppose there is an integer $N$ such that … in the unbounded version of LLE, or … in the bounded version. Let…

Asymptotic velocity conjecture. As $t\to 0$, the quotient $P(t,x)/\ln t$ should approach a limit $k=k(x)$, and $k(x)$ should belong to $[0,1)$ except on a set of exceptional values…