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We present an exact sampling method for the first passage event of a Levyprocess. The idea is to embed the process into another one whose first passageevent can be sampled exactly, and then recover the part belonging to the formerfrom the latter. The method is based on several distributional properties thatappear to be new. We obtain general procedures to sample the first passageevent of a subordinator across a regular non-increasing boundary, and that of aprocess with infinite Levy measure, bounded variation, and suitable driftacross a constant level or interval. We give examples of application to arather wide variety of Levy measures.

On exact sampling of the first passage event of Levy process with infinite Levy measure and bounded variation