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2010 The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6
Ivan Nourdin, Anthony Réveillac, Jason Swanson
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Electron. J. Probab. 15: 2117-2162 (2010). DOI: 10.1214/EJP.v15-843

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 $\int\!g(B(s))\,dB(s)$ 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 $B$.

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Ivan Nourdin. Anthony Réveillac. Jason Swanson. "The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6." Electron. J. Probab. 15 2117 - 2162, 2010. https://doi.org/10.1214/EJP.v15-843

Information

Accepted: 14 December 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1225.60089
MathSciNet: MR2745728
Digital Object Identifier: 10.1214/EJP.v15-843

Subjects:
Primary: 60H05
Secondary: 60G15, 60G18, 60J05

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