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 H. Panzo (Séminaire de Probabilités L, 2019). 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.

arXiv comment16 pages, in v2 several errors where fixed and the main result has been established by an alternative argument