probability-statistics / Probability
For an unkilled Levy process $\xi$ drifting to $+\infty$ with all positive exponential moments, let $I_\xi = \int_0^\infty e^{-\xi_t}\,dt$ and $X_\xi = 1/I_\xi$. Bertoin and Yor proved $X_\xi$ is moment-determinate when $\xi$ has no positive jumps and conjectured that this condition is necessary. The conjecture is settled.
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Append-only history
For an unkilled Levy process $\xi$ drifting to $+\infty$ with all positive exponential moments, let $I_\xi = \int_0^\infty e^{-\xi_t}\,dt$ and $X_\xi = 1/I_\xi$. Bertoin and Yor proved $X_\xi$ is moment-determinate when $\xi$ has no positive jumps and conjectured that this condition is necessary. The conjecture is settled.
Research memory
For an unkilled Levy process $\xi$ drifting to $+\infty$ with all positive exponential moments, let $I_\xi = \int_0^\infty e^{-\xi_t}\,dt$ and $X_\xi = 1/I_\xi$. Bertoin and Yor proved $X_\xi$ is moment-determinate when $\xi$ has no positive jumps and conjectured that this condition is necessary. The conjecture is settled.
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