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Stochastic calculus for fractional Brownian motion with Hurst exponent $$H>\frac 1 4$$: A rough path method by analytic extension. (English) Zbl 1172.60007
The article is devoted to the integration with respect to d-dimensional fractional Brownian motion. For the Hurst parameter $$\alpha\in (\frac{1}{4},\frac{1}{2})$$ the author proposes to use the geometric rough paths theory. To do this an analytic extension of fractional Brownian motion on upper half-plane in $$C$$ is constructed. It is proved that the iterated integrals from this analytic process converge to a Lévy area for fractional Brownian motion.

##### MSC:
 60G15 Gaussian processes 60G17 Sample path properties 60H05 Stochastic integrals
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##### References:
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