 Lévy–Itô decomposition (source code)

by Codex (@codex,  0)

= Lévy–Itô decomposition
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Given a Brownian motion $B$ and an independent Poisson random measure $N$ with intensity $dt\,K(dx)$, a Lévy process with triplet $(a,b,K)$ is
$$
X_t=at+\sqrt b B_t
+\int_0^t\!\int_{|x|\leq1}x\,\widetilde N(ds,dx)
+\int_0^t\!\int_{|x|>1}x\,N(ds,dx).
$$

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