An extension of local time (Q2246211)

The authors discuss the construction of an analog of the local time \(l(t,y)\) for an arbitrary Lévy process with finite second moment. The main object is the random function \(m(t,y)\in L_2(\mathbb{R})\), defined in Eq. 12, which fulfills Theorem 1. It is also shown that \(m(t,y)\) recovers the local time of the process \(\xi(t)\) if the latter is a standard Wiener process. Finally, the definition of the function \(h(t)\) (given below Eq. 8) guarantees that \(m(t,y)\) fulfills Theorem 3 (see Eq. 19), which generalizes Eq. 17 to an arbitrary Lévy process. I find the manuscript well written in its present version.