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Self-similar co-ascent processes and Palm calculus

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  • Mönch, Christian

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).

Suggested Citation

  • Mönch, Christian, 2024. "Self-similar co-ascent processes and Palm calculus," Stochastic Processes and their Applications, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:spapps:v:174:y:2024:i:c:s030441492400084x
    DOI: 10.1016/j.spa.2024.104378
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    References listed on IDEAS

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    1. Last, Günter & Thorisson, Hermann, 2015. "Construction and characterization of stationary and mass-stationary random measures on Rd," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4473-4488.
    2. Aurzada, Frank & Guillotin-Plantard, Nadine & Pène, Françoise, 2018. "Persistence probabilities for stationary increment processes," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1750-1771.
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