Let $B$ be Brownian motion and let $N(ds,dx)$ be an independent <Poisson random measure> with intensity $ds\,K(dx)$. Writing $\widetilde N=N-ds\,K(dx)$ for its compensated version, the <Lévy–Itô decomposition> constructs
$$
\boxed{
X_t=at+\sqrt b B_t
+\int_0^t\!\int_{|x|\leq1}x\,\widetilde N(ds,dx)
+\int_0^t\!\int_{|x|>1}x\,N(ds,dx).}
$$
The four terms are independent drift, Gaussian, compensated small-jump and compound-Poisson large-jump components.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-201/6/c/solution