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The law of a stochastic integral with two independent fractional Brownian motions. (English) Zbl 1173.60324

Summary: Using the tools of the stochastic integration with respect to the fractional Brownian motion, we obtain the expression of the characteristic function of the random variable \(\int_{0}^{1}B^{\alpha }_{s}dB^{H}_{s}\) where \(B^{\alpha }\) and \(B^{H}\) are two independent fractional Brownian motions with Hurst parameters \(\alpha\in(0,1) \) and \(H>\frac12\) respectively. The two-parameter case is also considered.

MSC:

60H05 Stochastic integrals
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