Abstract
We consider Riemann sum approximations of stochastic integrals with respect to the fractional Browian motion of index . We show the convergence of these schemes at first and second order. The processes obtained in the limit in the second case are stochastic integrals with respect to the Rosenblatt process if and the standard Brownian motion otherwise. These results are obtained under the assumption that the integrand is a “controlled” process. We provide many examples of such processes, in particular fractional semimartingales and multiple Wiener-Itô integrals.
Funding Statement
I. Nourdin and V. Garino are supported by the FNR OPEN grant APoGEe at Luxembourg University.
Acknowledgments
We heartily thank the editorial board and the two reviewers, whose comments and careful reading led to a drastic change from the original version and significantly improved the readability of the article.
Citation
Valentin Garino. Ivan Nourdin. Pierre Vallois. "Asymptotic error distribution for the Riemann approximation of integrals driven by fractional Brownian motion." Electron. J. Probab. 27 1 - 43, 2022. https://doi.org/10.1214/22-EJP852
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