An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter

By Christian Bender. 2003

148 citations recorded by the source corpus.

We consider fractional Brownian motions BtH with arbitrary Hurst coefficients 0<H<1 and prove the following results: (i) An integral representation of the fractional white noise as generalized Wiener integral; (ii) an Ito formula for generalized functionals of BtH; (iii) an analogue of Tanaka's formula; (iv) a Clark–Ocone formula for Donsker's delta function of BtH; (v) an integral representation of the local time of BtH.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/47919482d62236c49a0eb385badfcc4323b44bdd

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Citations in the corpus

Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H∈(0,12) (2005, methodology): “Whereas in [4]f does not need to be a twice continuously differentiable or convex function, it cannot to fast at infinity.”
Skorohod integration and stochastic calculus beyond the fractional Brownian scale (2005, methodology): “…to be uniquely defined, and to be useful: an Ito formula is established; it is employed to derive a Tanaka formula for a corresponding local time; linear additive and multiplicative stochastic differential equations are solved; an analysis of existence for the stochastic heat equation is given.”
Stochastic Calculus with Respect to Gaussian Processes (2014, background): “The reader interested in an exhaustive overview of the subject may refer to [10, 37, 43] for divergence type integral and to [4, 7, 11, 42] for integral in the white noise theory framework.”