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

In this paper, we consider the derivatives of intersection local time for two independent d-dimensional symmetric alpha-stable processes X-alpha and (X) over tilde ((alpha) over tilde) with respective indices alpha and (alpha) over tilde. We first study the sufficient condition for the existence of the derivatives, which makes us obtain the exponential integrability and Holder 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.

Automated summary

In this paper, we consider the derivatives of intersection local time for two independent d-dimensional symmetric alpha-stable processes and study the sufficient and necessary conditions for their existence. We also investigate the power variation of the derivatives.