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

   
@article{EJP843,
	author = {Ivan Nourdin and Anthony Réveillac and Jason Swanson},
	title = {The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {15},
	year = {2010},
	keywords = {Stochastic integration; Stratonovich integral; fractional Brownian motion; weak convergence; Malliavin calculus},
	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 $B$.},
	pages = {no. 70, 2117-2162},
	issn = {1083-6489},
	doi = {10.1214/EJP.v15-843},    
        url = {http://ejp.ejpecp.org/article/view/843}}