Moments of last exit times for Lévy processes (Q1434445)

The paper analyzes some properties of the last exit time \(T\) from a ball with radius \(a\) for a transient Lévy process in \(R^d\). It is shown that the mathematical expectation of \(T^b\), \(b\) positive, is either finite for all \(a\), or infinite for all \(a\). Then the set \(F\) of \(b\) associated with the first case (i.e. finite for all \(a\)) is fully characterized by using the logarithm of the characteristic function of the Lévy variable \(X(t)\). Further results on \(F\) are described in terms of the one-sided moment of \(X(t)\).