m-order integrals and generalized Ito's formula; the case of a fractional Brownian motion with any Hurst index

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Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion (2006, background): “1 in [9], we can prove that, when H < 1/2:”
Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: The critical case H=1/4 (2008, background): “By Theorem 3 in [17] (see also [3, 8, 9]), we have that ∫ 1”
Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H∈(0,12) (2005, background): “3) was simultaneously and indepen discovered in the paper [13] by Gradinaru, Nourdin, Russo and Vallois.”
Variations of the solution to a stochastic heat equation (2005, methodology): “In [7] and [2], it is shown that the symmetric integral ∫ (B1/6) 2 dB1/6 does not exist.”
Elements of Stochastic Calculus via Regularization (2006, methodology): “Using more sophisticated integrals via regularization, other types of Itô formulae can be written for any H in ]0, 1[; see [26].”
Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion (2008, methodology): “This stochastic integral satisfies the zero mean property and it can be expressed as the limit of Riemann sums defined using Wick products. ii) The pathwise Riemann–Stieltjes integral ∫ T 0 vsdB H s exists if vt t ∈ 0 T is a stochastic process with Hölder continuous paths of order > 1−H , as a…”