LEVY PROCESSES, GENERALIZED MOMENTS AND UNIFORM INTEGRABILITY

We give new proofs of certain equivalent conditions for the existence of generalized moments of a Levy process (X-t)(t >= 0); in particular, the existence of a generalized g-moment is equivalent to the uniform integrability of (g(X-t))(t is an element of[0,1]). As a consequence, certain functions of a Levy process which are integrable and local martingales are already true martingales. Our methods extend to moments of stochastically continuous additive processes, and we give new, short proofs for the characterization of lattice distributions and the transience of Levy processes.

Automated summary

In this paper, new proofs are presented for the existence of generalized moments of a Levy process, along with the equivalent conditions and consequences. The methods can also be extended to moments of stochastically continuous additive processes, and new proofs for the characterization of lattice distributions and the transience of Levy processes are provided.