An Introduction to (Stochastic) Calculus with Respect to Fractional Brownian Motion

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Pathwise integration and change of variable formulas for continuous paths with arbitrary regularity (2018, background): “Integration theory and change of variables formulas for processes with infinite quadratic variation, such as fractional Brownian motion and other fractional processes, have relied on probabilistic, rather than pathwise constructions [5, 9, 18].”
Fractional stochastic differential equations with applications to finance (2013, background): “This kind of fractional stochastic integral belongs to the third approach mentioned above and turns out to be equal to the divergence integral plus a complementary term (see Remark 18 in [6]).”
MULTIFRACTIONAL STOCHASTIC VOLATILITY MODELS (2011, unknown): “Various approaches have been developed since, based mainly on Malliavin calculus [25, 2], pathwise integrals [65], rough paths [24], and white noise theory [31, 12, 10].”
Stochastic Calculus with Respect to Gaussian Processes (2014, background): “The reader interested in an exhaustive overview of the subject may refer to [10, 37, 43] for divergence type integral and to [4, 7, 11, 42] for integral in the white noise theory framework.”