Take the tour ×  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.   share|improve
this question add comment  1 Answer  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).  share|improve this
answer Thanks you. Is it possible that $\nu(x)$ is decreasing
for certain values of x? Obviously this would imply that the
random variable is not infinitely divisible. –  Fantastic Mr.
Fox Apr 24 '12 at 13:33 I don't understand what you're asking,
since $\nu$ is a measure. What