Bertoin-Yor Moment Determinacy Conjecture

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.

Result: Proved
Status: Resolved
AI contribution: AI-assisted
Method: Argument
Field: Probability
Posed by: Jean Bertoin, Marc Yor
Year posed: 2002
Years open: 24y
Solved: 2026-06-30
Model: GPT-5.4 Thinking, GPT-5.5 Thinking and Pro
Vendor: OpenAI
Collaborators: Martin Minchev
Verification: Unreviewed
Publication: Preprint
Significance: 15 / 100
Disclosed cost: —
Wikipedia: No dedicated article

What the AI did

The paper has a dedicated Use of AI tools section stating the models were used during the exploratory and editorial stages of the work. Exploration is mathematical work rather than prose work, but no individual step is attributed, so the lowest tier applies.

Verification

Single-author arXiv preprint; not yet peer-reviewed.

Source

arXiv:2607.00132 - On a moment determinacy conjecture of Bertoin and Yor

Bertoin-Yor Moment Determinacy Conjecture

What the AI did

Verification

Source

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