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Mandelbrot introduced fractional Brownian motion as a model for many long memory processes of which I am particularly interested in stochastic latent volatility.  David Nualart has proven that stochastic integration with respect to fractional Brownian motion is Besov $B^s_{p,q}$ with appropriate restrictions on $p,q,s$.   He does so here: NualartBesovRegularityFBM.  This allows us to use filtering of stochastic volatility using the Donoho-Johnstone wavelet thresholding.  We already have empirical results suggesting the universality of long memory, i.e. Hurst > 1/2, for stocks and commodities.  Therefore we have a well-founded arbitrage in options.