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Bertoin-Yor Moment Determinacy Conjecture

Probability & statistics · posed by Jean Bertoin, Marc Yor, 2002 · solved

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Statement

For an unkilled Levy process ξ\xi drifting to +∞+\infty with all positive exponential moments, let Iξ=∫0∞e−ξt dtI_\xi = \int_0^\infty e^{-\xi_t}\,dt and Xξ=1/IξX_\xi = 1/I_\xi. Bertoin and Yor proved XξX_\xi is moment-determinate when ξ\xi has no positive jumps and conjectured that this condition is necessary. The conjecture is settled.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Martin Minchev, using GPT-5.4 Thinking, GPT-5.5 Thinking and Pro

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