Universality of persistence exponents for fractionally integrated Lévy processes

For each $\beta\ge0$, consider a $\beta$-fractionally integrated Lévy process and let $\theta(\beta)$ be its persistence exponent. The Lévy universality conjecture. For every $\beta\ge0$, the exponent $\theta(\beta)$ is the same for all $\beta$-fractionally integrated Lévy processes with finite variance.

This extends a theorem requiring exponential moments in a neighborhood of zero; the finite-variance formulation is posed as an open conjecture.