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      Functional It\^o formula for fractional Brownian motion

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          Abstract

          We develop the functional It\^o/path-dependent calculus with respect to fractional Brownian motion with Hurst parameter \(H> \frac{1}{2}\). Firstly, two types of integrals are studied. The first type is Stratonovich integral, and the second type is Wick-It\^o integral. Then we establish the functional It\^o formulas for fractional Brownian motion, which extend the functional It\^o formulas in Dupire (2009) and Cont-Fourni\'e (2013) to the case of non-semimartingale. Finally, as an application, we deal with a class of fractional backward stochastic differential equations (BSDEs). A relation between fractional BSDEs and path-dependent partial differential equations (PDEs) is established.

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          Stochastic analysis of fractional brownian motions

          S Lin (1995)
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            Itô's formula with respect to fractional Brownian motion and its application

            Fractional Brownian motion (FBM) with Hurst index1/2
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              Backward Stochastic Differential Equation Driven by Fractional Brownian Motion

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                Author and article information

                Journal
                2016-06-04
                2016-08-02
                Article
                1606.01442
                9c21d6e4-483c-49f0-93c4-18990257d059

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                60H05, 60H07, 60G22
                16 pages
                math.PR

                Probability
                Probability

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