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 $B$.
"The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6." Electron. J. Probab. 15 2117 - 2162, 2010. https://doi.org/10.1214/EJP.v15-843