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}
}
  • Ivan Nourdin, Anthony Reveillac, J. Swanson
  • 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
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