Weak symmetric integrals with respect to the fractional Brownian motion

2016/06/13 by Binotto, Giulia, Nourdin, Ivan, Nualart, David
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1606.04046

Abstract

The aim of this paper is to establish the weak convergence, in the topology of the Skorohod space, of the ν-symmetric Riemann sums for functionals of the fractional Brownian motion when the Hurst parameter takes the critical value H=(4ℓ+2)^-1, where ℓ=ℓ(ν)≥ 1 is the largest natural number satisfying ∫₀¹ α^2jν(dα)=(2j+1)^-1 for all j=0,…,ℓ-1. As a consequence, we derive a change-of-variable formula in distribution, where the correction term is a stochastic integral with respect to a Brownian motion that is independent of the fractional Brownian motion.

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