Self-similar co-ascent processes and Palm calculus

Christian Mönch

Stochastic Processes and their Applications, 2024, vol. 174, issue C

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 α-stable Lévy-subordinators with α∈(0,1).

Keywords: Brownian ascent; Brownian meander; First passage times; Self-similar processes; Palm distribution; Stable subordinator (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104378

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