A transitivity property of Ocone martingales

Jichen Zhang and Zengjing Chen

Statistics & Probability Letters, 2023, vol. 193, issue C

Abstract: This paper gives a sufficient condition to make an Ocone martingale still an Ocone martingale after an integral transformation. Let θ be an Ocone martingale, Mt=∫0tαsdθs. Then M is an Ocone martingale if α and θ are conditionally independent given 〈θ〉. The converse problem is still open, but a partial converse theorem is obtained for a special class of Ocone martingales, which greatly generalizes Theorem 3 proposed by Vostrikova and Yor (2000). The results of this paper can be used to determine whether a local martingale is an Ocone martingale, as well as to construct more complex examples of Ocone martingales.

Keywords: Ocone martingale; Conditional independence; Stochastic integral; Dambis–Dubins–Schwarz Brownian motion (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2022.109703

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