Derivatives of intersection local time for two independent symmetric alpha-stable processes

In this talk, we consider the derivatives of intersection local time for two independent d-dimensional symmetric alpha-stable processes. We first study the sufficient condition for the existence of the derivatives, which makes us obtain the exponential integrabilityand Holder continuity. Then we show that this condition is also necessary for the existence of derivatives of intersection local time at the origin. As a related problem, we also study the power variation of the derivatives.