Event Series
Event Type
Seminar
Monday, May 6, 2019 4:00 PM
Steven Evans (UC Berkeley)

The α-Lipschitz minorant of a function is the greatest α-Lipschitz function dominated pointwise by the function, should such a function exist. I 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. I 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, I will elucidate the probabilistic structure of both a “generic” excursion and the special excursion that straddles the time zero.