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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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