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.
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Mohamed El Omari (2021) studied this question.
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