Mixtures of higher-order fractional Brownian motions

Mohamed El Omari

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 12, 4200-4215

Abstract: In this article, we show that the nth-order fractional Brownian motions (fBm) introduced by Perrin et al. are non Markovian special semimartingales. Their infinite mixtures are also presented and shown to be semimartingales satisfying mixed self-similarity property and accounting for long-range dependence phenomena. As result, they are alternative to mixed fBm in modeling stock prices in arbitrage-free financial markets.

Date: 2023
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DOI: 10.1080/03610926.2021.1986541

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