Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 201 / 6 / b / Solution

The Lévy–Khintchine theorem states that there is a unique triplet $(a,b,K)$, where $a\in \mathbb{R}$, $b\ge 0$, and $K$ is a measure on $\mathbb{R}\setminus \{0\}$ satisfyingsuch thatConversely every such triplet is the characteristic triplet of a Lévy process.