Fractional Hida Malliavin Derivatives and Series Representations of Fractional Conditional Expectations

Sixian Jin; Qidi Peng; Henry Schellhorn

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arXiv · 1406.1538

Fractional Hida Malliavin Derivatives and Series Representations of Fractional Conditional Expectations

Sixian Jin·Qidi Peng·Henry Schellhorn

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Abstract

We represent fractional conditional expectations of a functional of fractional Brownian motion as a convergent series in L^2 space. When the target random variable is some function of a discrete trajectory of fractional Brownian motion, we obtain a backward Taylor series representation; when the target functional is generated by a continuous fractional filtration, the series representation is obtained by applying a "frozen path" operator and an exponential operator to the functional. Three examples are provided to show that our representation gives useful series expansions of ordinary expectations of target random variables.

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BibTeX RIS

Sixian Jin, Qidi Peng, Henry Schellhorn. 2014-06-05. Fractional Hida Malliavin Derivatives and Series Representations of Fractional Conditional Expectations. https://arxiv.org/abs/1406.1538

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