PUB - Publikationen an der Universität Bielefeld

Consider a stable L,vy process and let , for , denote the first passage time of above the level . In this work, we give an alternative proof of the absolute continuity of the law of and we obtain a new expression for its density function. Our constructive approach provides a new insight into the study of the law of . The random variable , defined as the limit of when the corresponding overshoot tends to , plays an important role in obtaining these results. Moreover, we establish a relation between the random variable and the dual process conditioned to die at . This relation allows us to link the expression of the density function of the law of presented in this paper to the already known results on this topic.