The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6

2010/06/22 by Nourdin, Ivan, Réveillac, Anthony, Swanson, Jason
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1006.4238

Abstract

Let B be a fractional Brownian motion with Hurst parameter H=1/6. It is known that the symmetric Stratonovich-style Riemann sums for ∫ 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.

Related

• The calculus of differentials for the weak Stratonovich integral
• Weak symmetric integrals with respect to the fractional Brownian motion
• A Stratonovich-Skorohod integral formula for Volterra Gaussian rough paths
• The isometry of symmetric-Stratonovich integrals w.r.t. Fractional Brownian motion H< (1)/(2)
• An extension of the stochastic sewing lemma and applications to fractional stochastic calculus