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Guerra, João; Nualart, David

Stochastic differential equations driven by fractional Brownian motion and standard Brownian motion. (English) Zbl 1151.60028

Stochastic Anal. Appl. 26, No. 5, 1053-1075 (2008).
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)].

Cited in 68 Documents

MSC:

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

Keywords:

fractional Brownian motion; stochastic differential equations

Citations:

Zbl 0236.60037; Zbl 0229.60039
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\textit{J. Guerra} and \textit{D. Nualart}, Stochastic Anal. Appl. 26, No. 5, 1053--1075 (2008; Zbl 1151.60028)
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References:

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