Self-similar co-ascent processes and Palm calculus

Abstract

We study certain renormalised first passage bridges of self-similar processes, generalising the “Brownian co-ascent process” discussed by Panzo (Sém. Prob. L, 2019) and introduced by Rosenbaum and Yor (Sém. Prob. XLVI, 2014). We provide a characterisation of co-ascent processes via Palm measures, namely that the co-ascent of a self-similar process is the process under the Palm distribution associated with its record measure. We use this representation to derive a distributional identity for -stable Lévy-subordinators with 𝛼 ∈ (0, 1).