Self-similar co-ascent processes and Palm calculus

Abstract

We discuss certain renormalised first passage bridges of self-similar processes. These processes generalise the Brownian co-ascent, a term recently introduced by Panzo [Panzo, H. (2018). "Scaled penalization of Brownian motion with drift and the Brownian ascent", arXiv preprint arXiv:1803.04157]. Our main result states that the co-ascent of a given process is the process under the Palm distribution of its record measure. We base our notion of Palm distribution on self-similarity, thereby complementing the more common approach of considering Palm distributions related to stationarity or stationarity of increments of the underlying processes.Comment: 14 page