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Stochastic differential equations driven by fractional Brownian motion and standard Brownian motion. (English) Zbl 1151.60028
Summary: We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter \(H > 1/2\) and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration and the classical Itô stochastic calculus. The existence result is based on the theorem of S. Yamada and T. Watanabe [J. Math. Kyoto Univ. 11, 155–167 (1971; Zbl 0236.60037); J. Math. Kyoto Univ. 11, 553–563 (1971; Zbl 0229.60039)].

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H05 Stochastic integrals
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