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arXiv · 2312.13805

Revisiting the identification problem of a function by the ratio of Laplace transforms of powers

Dongdong Hu·Linglong Yuan·Minzhi Zhao
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Abstract

The ratio of Laplace transforms of powers of a function arises in the context of auction theory. The question whether a function is uniquely identified by this ratio has been answered affirmatively, if the function is non-negative, non-decreasing and right analytic.This paper extends the result to a larger class of functions without monotonicity.A conjecture in the literature says that all c\`adl\`ag functions can be identified by the ratio. We disprove this conjecture by providing simple functions that cannot be identified.

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Dongdong Hu, Linglong Yuan, Minzhi Zhao. 2023-12-21. Revisiting the identification problem of a function by the ratio of Laplace transforms of powers. https://arxiv.org/abs/2312.13805

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