Tanaka formula for the fractional Brownian motion

By Laure Coutin, David Nualart, Ciprian A. Tudor. 2001

80 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/604e6737b84ca6eccd810d37b805526290ab322f

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Citations in the corpus

Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H>=1/4 (2003, methodology): “We recall also that, for H > 1 3 , a Tanaka type formula has been obtained by [9] involving Skorohod integral.”
Wiener integrals, Malliavin calculus and covariance measure structure (2006, unknown): “• the proof of the Tanaka formula involving weighted local times; for the fBm case, this has been proved in [ 8 ] but the proofs necessitates the expression of the kernel K.”
Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H∈(0,12) (2005, background): “All rights reserved. doi:10.1016/j.anihpb.2004.09.004 a waran at on ity Zähle lassical integral gence opnd Tudor e e korohod integral, n st chastic rownian in [3]. rgence ns, Hu 1.”
An Introduction to (Stochastic) Calculus with Respect to Fractional Brownian Motion (2007, background): “In Proposition 2 of [ CNT01 ], Coutin, Nualart, and Tudor give the Wiener chaos expansion of this weighted local time.”
Skorohod integration and stochastic calculus beyond the fractional Brownian scale (2005, methodology): “On the other hand, and more recently, several stochastic analysts working on fractional Brownian motion have chosen to consider a dierent occupation measure because it yields a connection to stochastic calculus via the It^ o-Tanaka formula: see for example [ 8 ]; also see the summary on local time f”
Sample path properties of bifractional Brownian motion (2006, background): “[16], Hu and Oksendal [22] and Eddahbi et al.”
An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter (2003, methodology): “As an application we obtain an extension of the Tanaka formula that was also proven by Hu and Iksendal (2001) and Coutin et al. (2001) for the special cases 12 ¡H ¡ 1, and 13 ¡H ¡ 1, respectively.”
Stochastic Calculus with Respect to Gaussian Processes (2014, background): “8] (see also references therein, in particular [CNT01]).”