Lipschitz Minorants of Lévy Processes

Seminar: Probability Seminar | February 26 | 3:10-4 p.m. | 330 Evans Hall

 Mehdi Ouaki, U.C. Berkeley

 Department of Statistics

The \alpha-Lipschitz minorant of a function is the greatest \alpha-Lipschitz function dominated pointwise by the function, should such a function exist. We will discuss this construction when the function is a sample path of a (2-sided) Lévy process. The contact set is the random set of times when the sample path touches the minorant. This is a stationary, regenerative set. We will provide a description of the excursions of the sample path away from the contact set that is analogous to Itô’s theory for the excursions of a Markov process away from some point in the state space. In particular, we provide the probabilistic structure of both a “generic” excursion and the special excursion that straddles the time zero.