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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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