The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6

Abstract : Let B be a fractional Brownian motion with Hurst parameter H=1/6. It is known that the symmetric Stratonovich-style Riemann sums for $\int g(B(s))dB(s)$ do not, in general, converge in probability. We show, however, that they do converge in law in the Skorohod space of càdlàg functions. Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correction term that is an ordinary Itô integral with respect to a Brownian motion that is independent of B.
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Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2010
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Ivan Nourdin, Anthony Réveillac, Jason Swanson. The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2010. <hal-00493981>

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