= Uncompensated Lévy–Khintchine formula
{title2=$\psi(u)=ibu-\sigma^2u^2/2+\int(e^{iuy}-1)K(dy)$}
If a <Lévy measure> satisfies $\int_{|y|\le1}|y|K(dy)<\infty$, the jump integral in the <Lévy–Khintchine formula> can be written without compensation: $\mathbb E e^{iuX_t}=e^{t\psi(u)}$, with the displayed exponent. Its integral is absolutely convergent because $|e^{iuy}-1|\le|u||y|$ near zero and is at most $2$ elsewhere. If the compensated formula uses drift $\gamma$, the uncompensated drift is $b=\gamma-\int_{|y|\le1}yK(dy)$. The Gaussian coefficient is still $\sigma^2\ge0$.
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