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Regularity of an abstract Wiener integral

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  • Hannebicque, Brice
  • Herbin, Érick

Abstract

In this article, we propose a way to study sample path properties of processes indexed by a general poset (T,≼). This framework encompasses large classes of vector spaces, manifolds and continuous R-trees. We define a Wiener-type integral Yt=∫≼tfdX for all t∈T, a deterministic function f:T→R and a set-indexed Lévy process X. Bounds for the Hölder regularity of Y are given which indicate how the regularities of f and X contributes to that of Y. This work is a continuation of Herbin and Richard (2016) and extends those of Jaffard (1999) and Balança and Herbin (2012).

Suggested Citation

  • Hannebicque, Brice & Herbin, Érick, 2022. "Regularity of an abstract Wiener integral," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 154-196.
    • Handle: RePEc:eee:spapps:v:154:y:2022:i:c:p:154-196
    DOI: 10.1016/j.spa.2022.09.002
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    References listed on IDEAS

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    1. Herbin, Erick & Merzbach, Ely, 2013. "The set-indexed Lévy process: Stationarity, Markov and sample paths properties," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1638-1670.
    2. Herbin, Erick & Lévy-Véhel, Jacques, 2009. "Stochastic 2-microlocal analysis," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2277-2311, July.
    3. Adler, R. J. & Monrad, D. & Scissors, R. H. & Wilson, R., 1983. "Representations, decompositions and sample function continuity of random fields with independent increments," Stochastic Processes and their Applications, Elsevier, vol. 15(1), pages 3-30, June.
    4. Balança, Paul & Herbin, Erick, 2012. "2-microlocal analysis of martingales and stochastic integrals," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2346-2382.
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