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Stochastic calculus provides a consistent theory of integration for stochastic processes and is used to model random systems. Its applications range from statistical physics to quantitative finance.
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A simple decomposition for fractional Brownian motion with parameter $H<1/2$
It looks like this idea isn't new. There is something very similar in an article by Alos, Mazet, and Nualart (SPA 2000).
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A simple decomposition for fractional Brownian motion with parameter $H<1/2$
Interesting, I don't think I've seen that before.
But there is a similar sort of decomposition in W. Li and W. Linde 1998, however I don't think it's quite the same. Cheridito 2003 (Mixed-FBM) tackles …