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The weak stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6. (English) Zbl 1225.60089
Summary: 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 $$B$$.

##### MSC:
 60H05 Stochastic integrals 60G22 Fractional processes, including fractional Brownian motion 60F05 Central limit and other weak theorems 60H07 Stochastic calculus of variations and the Malliavin calculus
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