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

@article{Nourdin2010TheWS,
title={The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6},
author={Ivan Nourdin and Anthony Reveillac and J. Swanson},
journal={Electronic Journal of Probability},
year={2010},
volume={15},
pages={2117-2162}
}
• Published 2010
• Mathematics
• Electronic Journal of Probability
• 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 cadlag functions. Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correction term that is an ordinary Ito integral with respect to a Brownian motion that is… CONTINUE READING