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The Levy-Khintchine formula gives a triple $(a,\sigma,\nu)$ for the characteristic exponent $\Psi(s)$ of an infinitely divisible random variable where

\Psi(s)=ias + \frac{1}{2}\sigma^2s^2 + \int_{\mathbb{R}}(1-e^{isx} + is\mathbb{1}_{|x|<1})d\nu(x)

My question is whether $\nu$ is unique? Or whether it is only the unique Levy measure?

Are there references in the literature to this fact.

Thanks

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Yes, there is a one-to-one correspondance between infinitely divisble distributions and the triple $(a,\sigma,\nu)$ given by the Lévy-Khintchine formula. You can have a look at Lévy Processes and Infinitely Divisible Distributions by Ken Iti Sato (Theorem 8.1).

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    Thank you for your time Stefan. Yes I was curious whether $\nu$ could be a signed measure.2012-04-30