Potentials of Stable Processes

  • A. E. Kyprianou
  • A. R. Watson
Part of the Lecture Notes in Mathematics book series (LNM, volume 2123)


For a stable process, we give an explicit formula for the potential measure of the process killed outside a bounded interval and the joint law of the overshoot, undershoot and undershoot from the maximum at exit from a bounded interval. We obtain the equivalent quantities for a stable process reflected in its infimum. The results are obtained by exploiting a simple connection with the Lamperti representation and exit problems of stable processes.


Lévy processes Stable processes Reflected stable processes Hitting times Positive self-similar Markov processes Lamperti representation Potential measures Resolvent measures 

AMS classification (2000):

60G52 60G18 60G51 



We would like to thank the referee for his careful reading of this paper.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.University of BathBathUK
  2. 2.University of ZürichZürichSwitzerland

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