Hunt's hypothesis (H) and Getoor's conjecture for Lévy processes (Q429286)

Let \(X\) be a Lévy process on \(\mathbb R^n\), with Lévy-Khinchin exponent \((a, A, \mu )\). The authors prove the following results concerning the fact that \(X\) satisfies Hunt's hypothesis \((H)\):NEWLINENEWLINE(i) if the matrix \(A\) is non-degenerate, then \(X\) satisfies \((H)\);NEWLINENEWLINE(ii) if \(\mu (\mathbb R^n \setminus \sqrt{A} \mathbb R^n) < \infty \), then \(X\) satisfies \((H)\) iff the equation NEWLINE\[NEWLINE\sqrt{A} y = - a - \int _ {\{x \in \mathbb R^n \setminus \sqrt{A} \mathbb R^n; |x| < 1 \} } x \mu (d x) NEWLINE\]NEWLINE has at least one solution \(y \in \mathbb R^n\);NEWLINENEWLINE(iii) if \(X\) is a subordinator and satisfies \((H)\), then its drift coefficient is \(0\).