Derivatives of Intersection Local Time for Two Independent Symmetric α-stable Processes

Abstract

In this paper, we consider the derivatives of intersection local time for two independent d-dimensional symmetric α-stable processes X^α and \({\widetilde X^{\widetilde \alpha }}\) with respective indices α and \(\widetilde \alpha \). We first study the sufficient condition for the existence of the derivatives, which makes us obtain the exponential integrability and Hölder continuity. Then we show that this condition is also necessary for the existence of derivatives of intersection local time at the origin. Moreover, we also study the power variation of the derivatives.