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 Stratonovichstyle 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 $B$.
 Publication:

arXiv eprints
 Pub Date:
 June 2010
 arXiv:
 arXiv:1006.4238
 Bibcode:
 2010arXiv1006.4238N
 Keywords:

 Mathematics  Probability
 EPrint:
 45 pages