Regularity of an abstract Wiener integral

Brice Hannebicque and Érick Herbin

Stochastic Processes and their Applications, 2022, vol. 154, issue C, 154-196

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).

Keywords: Sample path properties; Hölder regularity; Set-indexed process; Stochastic integral; Random measure; Lévy process; Stationarity (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:154:y:2022:i:c:p:154-196

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DOI: 10.1016/j.spa.2022.09.002

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