Asymptotic error distribution for the Riemann approximation of integrals driven by fractional Brownian motion

2020/05/06 by Valentin Garino, Garino, Valentin, Ivan Nourdin +3
Economics, Econometrics and Finance · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2005.02621

openalex publication_date 2020/05/06 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We consider Riemann sum approximations of stochastic integrals with respect to the fractional Browian motion of index H≥ \frac12. 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 H >\frac34 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

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